Progress of iteration theory since 1981



This survey tries to highlight a number of recent developments in iteration theory, and to point out a number of unsolved problems, thus also trying to predict the direction the evolution may take.


Cellular Automaton Composition Operator Formal Power Series Iteration Group Semi Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [Aczél 49]
    Aczél, J., Einige aus Funktionalgleichungen zweier Veränderlichen ableitbare Differentialgeichungen. Acta Sci. Math. (Szeged) 13 (1949), 179–189.Google Scholar
  2. [Aczél 91]
    Aczél, J., Remarks on a problem of Gy. Targonski. Report of the 27th ISFE, Poland 1989. Aequationes Math. 39 (1990), 314–315.CrossRefGoogle Scholar
  3. [Aczél, Gronau 88]
    Aczél, J., and Gronau, D., Some differential equations related to iteration theory. Canad. J. Math. 40 (1988), 695–717.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [Aczél, Gronau 881]
    Aczél, J. and Gronau, D., Iteration, translation, commuting and differential equations. In: Gronau, D. and L. Reich (eds), Selected topics in functional equations. [Grazer Math. Bericht Nr. 295], Math.Stat. Sekt. Forschungsges. Joanneum, Graz, 1988.Google Scholar
  5. [Agnes, Rasetti 88]
    Agnes, C. and Raserri, M., Complexity, undecidability and chaos: a class of dynamical systems with fractal orbits. In: Livi et al. (eds), Workshop on chaos and complexity, Torino, Oct. 5–11, 1987. World Scientific, Singapore, 1988, pp. 3–25.Google Scholar
  6. [Alsedá, Llibre, Misiurewicz 92]
    Alseda, LL., Llibre, J. and Misiurewicz, M., Combinatorial dynamics and entropy in dimension one. World Scientific, Singapore, 1992.Google Scholar
  7. [Alsina et al. 89]
    Alsina, C., Llibre, J., Mira, C., Simo, C., Targonski, GY. and Thibault, R., (eds), ECIT 87, Proc. Europ. Conf. on Iteration Th., Caldes de Malavella, Sept. 20–26, 1987. World Scientific, Singapore, 1989.Google Scholar
  8. [Barnsley 88]
    Barnsley, M., Fractals everywhere. Academic Press, New York, 1988.zbMATHGoogle Scholar
  9. [Bartels 91]
    Bartels, A., Über iterative Phantomwurzeln von Abbildungen (On iterative phantom roots of mappings). Diploma ( M.Sc.) Thesis, Universität Marburg, 1991.Google Scholar
  10. [Blanchard 84]
    Blanchard, P., Complex analytic dynamics of the Riemann sphere. Bull. Amer. Math. Soc. 11 (1984), 95–141.MathSciNetCrossRefGoogle Scholar
  11. Blažková, R. and Chvalina, J., Regularity and transivity of localautomorphism semigroups of locally finite forests. Arch. Math. (Brno) 4, Scripta Fac. Sci. Nat. USEP Brunensis 20 (1984), 183–194.zbMATHGoogle Scholar
  12. [Böttcher, Heidler 92]
    Böttcher, A. and Heidler, H., Algebraic composition operators. Integral Equations Operator Theory 15 (1992), 390–411.CrossRefGoogle Scholar
  13. [Bourlet 97]
    Bourlet, C., Sur certaines équations analogues aux équations différentielles (On certain equations analogous to differential equations). C.R. Acad. Sci. Paris 124 (1978), 1431–1433.Google Scholar
  14. [Bourlet 971]
    Bourlet, C., Sur les transmutations (On transmutations). Bull. Soc. Math. France 25 (1897), 132–140.MathSciNetzbMATHGoogle Scholar
  15. [Burkart 82]
    Burkart, U., Zur Charakterisierung diskreter dynamischer Systeme (On characterization of discrete dynamical systems). Ph.D. Thesis, Universität Marburg, 1982.Google Scholar
  16. [Cap 89]
    Cap, C. H., Two approaches to the iteration problem of diffeomorphisms. In [Alsina et al. 89], pp. 139–144.Google Scholar
  17. [Cap 91]
    Cap, C. H., Solving Abel, Jabotinsky and inverse ODE problems. In [Mira et al. 91], pp. 19–28.Google Scholar
  18. [Chvalina, Matoušková 84]
    Chvalina, J. and Matouskova, K., Coregularity of endomorphissm rnonoids of unars. Arch. Math. (Brno) 1, Scripta Fac. Sci. Nat. USEP Brunensis 20 (1984), 43–48.MathSciNetzbMATHGoogle Scholar
  19. [Collet, Eckmann 80]
    Collet, P. and Eckmann, J. P., Iterated maps on the interval as dynamical systems. Birkhäuser, Boston, 1980.zbMATHGoogle Scholar
  20. [Deslauriers, Dubuc 91]
    Deslauriers, G. and Dubuc, S., Continuous iterative iteration processes. In [Mira et al. 91], pp. 71–78.Google Scholar
  21. [Douady, Hubbard 84/85]
    Douady, A. and Hubbard, J., Etude dynamique de polynömes complexes (Dynamical study of complex polynomials) I, II. [Publ. Math. Orsay 84–02 and 85–04], Univ. d’Orsay, Orsay, 1984–85.Google Scholar
  22. [Dubuc 85]
    Dusuc, S., Functional equations connected with peculiar curves. In [Liedl et al. 85], pp. 33–40.Google Scholar
  23. [Ecalle 81]
    Ecalle, J., Les fonctions résurgents (On resurgent functions), vol. 1, 2, [Publ. Math. Orsay], Univ. d’Orsay, Orsay, 1981.Google Scholar
  24. [Ecalle 85]
    Ecalle, J., Iteration and analytic classification of local diffeomorphisms of C’. In [Lied(et al. 85], pp. 41–48.Google Scholar
  25. [Farmer et al. 85]
    Farmer, D. et al. (eds), Cellular automata. North Holland, Amsterdam, 1985.Google Scholar
  26. [Ferber 85]
    Ferber, R., Zelluläre Automaten als dynamische Systeme (Cellular automata as dynamical systems). Diploma ( M.Sc.) Thesis, Universität Marburg, 1985.Google Scholar
  27. [Ferber 88]
    Ferber, R., Räumliche und zeitliche Regelmäßigkeiten zellularer Automaten (Spatial and temporal regularities of cellular automata). Ph.D. Thesis, Universität Marburg, 1988.Google Scholar
  28. [Ferber 91]
    Ferber, R., Cellular automata are the continuous self-mappings of configuration spaces. In [Mira et ai. 91], pp. 79–85.Google Scholar
  29. [Ferber et al. 91]
    Ferber, R., Targonski, GY. and Weitkämper, J., Fractional-timestates of cellular automata. In [Mira et al. 91], pp. 86–106.Google Scholar
  30. [Förg-Rob 85]
    Förg-Rob, W., The Pilgerschritt transform in Lie algebras. In [Lied(et al. 85], pp. 59–71.Google Scholar
  31. [Förg-Rob 89]
    Förg-Rob, W., Some results on the Pilgerschritt transform. In [Alsina et al. 89], pp. 198–204.Google Scholar
  32. [Förg-Rob, Netzer 85]
    Förg-Rob, W. and Netzer, N., Product-integration and one-parameter subgroups of linear Lie groups. In [Liedl et al. 85], pp. 71–82.Google Scholar
  33. [Förg-Rob et al. 94]
    Förg-Rob, W., Gronau, D., Mira, C., Netzer, N. and Targonski, Gy., (eds), Proceedings of ECIT 92, Batschuns (Austria), September 1992. World Scientific, Singapore, 1994.Google Scholar
  34. [Gale 91]
    Gale, D., Conjectures. Math. Intelligencer 13 (1991), 53–55.MathSciNetCrossRefGoogle Scholar
  35. [Gardner 70]
    Gardner, M., Mathematical games. Scientific American, Oct. 1970 and Feb. 1971.Google Scholar
  36. [Graw 82]
    Gravi, R., Über die Orbitstruktur stetiger Abbildungen (On the orbit structure of continuous mappings.). Ph.D. Thesis, Universität Marburg, 1982.Google Scholar
  37. [Graw 84]
    Gravi, R., Compact orbits and periodicity. Nonlinear Anal. 8 (1984), 1473–1479.MathSciNetCrossRefGoogle Scholar
  38. [Gronau 91]
    Gronau, D., The Jabotinsky equations and the embedding problem. In [Mira et al. 91], pp. 138–148.Google Scholar
  39. [Gronau 911]
    Gronau, D., On the structure of the solution of the Jabotinsky equations in Banach spaces. Zeitschr. Anal. Anw. 10 (1991), 335–343.MathSciNetzbMATHGoogle Scholar
  40. [Gumowski, Mira 80]
    Gumowski, I. and Mira, C., Dynamique chaotique (Chaotic dynam- ics). Cepadues Editions, Toulouse, 1980.Google Scholar
  41. [Gumowski, Mira 80,]
    Gumowski, I. and Mira, C., Recurrences and discrete dynamic systems. [Springer Lecture Notes in Mathematics, Nr. 809], Springer, Berlin, 1980.Google Scholar
  42. [Isaacs 50]
    Isaacs, R., Iterates of fractional order. Canad. J. Math. 2 (1950), 409–416.MathSciNetzbMATHCrossRefGoogle Scholar
  43. [Jabotinsky 55]
    Jabotinsky, E., Iteration. Ph.D. Thesis, The Hebrew University, Jerusalem, 1955.Google Scholar
  44. [Jabotinsky 63]
    Jabotinsky, E., Analytic iteration. Trans. Amer. Math. Soc. 108 (1963), 457–477.MathSciNetzbMATHCrossRefGoogle Scholar
  45. [Krasner 38]
    Krasner, M., Une géneralisation de la notion de corps (A generalization of the notion of field). J. Pures Appl. 17 (1938), 367–385.zbMATHGoogle Scholar
  46. [Krause 88]
    Krause, G., Manuscript, 1988.Google Scholar
  47. [Kuczma, Choczewski, Ger 90]
    Kuczma, M., Choczewski, B. and Ger, R., Iterative functional equations. [Encyclopedia of Mathematics and its Applications, vol. 32], Cambridge University Press, Cambridge, 1990.Google Scholar
  48. [Lagarias 85]
    Lagarias, J. C., The 3x + 1 problem and its generalizations. American Math. Monthly 92 (1985), 3–23.MathSciNetzbMATHCrossRefGoogle Scholar
  49. [Lampreia, Sousa Ramos 91]
    Lampreia, J. P. and Sousa Ramos, J., Symbolic dynamics of trimodal maps. In [Mira et al. 91], pp. 184–193.Google Scholar
  50. [Lampreia et al. 93]
    Lampreia, J. P., Llibre, J., Mira, C., Sousa Ramos, J. and Targonski, GY. (eds), ECIT 91, Proc. Europ. Conf. on Iteration Theory, Lisbon Sep. 15–21, 1991. World Scientific, Singapore, 1993.Google Scholar
  51. [Langenberg 92]
    Langenberg, H., Zellulare Automaten und Iterationstheorie (Cellular automata and iteration theory). Diploma ( M.Sc.) Thesis, Universität Marburg, 1992.Google Scholar
  52. [Liedl 86]
    Liedl, R., Gruppenwertige Potenzreihen (Group valued power series). Anz. Österreich. Akad. Wiss. Math. Nat. K1. 1986, No. 5, 57–58.MathSciNetGoogle Scholar
  53. [Liedl, Netzer 89]
    Liedl, R. and Netzer, N., Group theoretic and differential geometric methods for solving the translation equation. In [Alsina et al. 89], pp. 240–252.Google Scholar
  54. [Liedl, Netzer 91]
    Liedl, R. and Netzer, N., Die Lösung der Translationsgleichung mittels schneller Pilgerschrittransformation (Solution of the translation equation by means of the fast Pilgerschritt transformation). [Grazer Ber. Nr. 314], Forschungsinst., Graz, 1991.Google Scholar
  55. [Lied], Netzer, Reitberger 81]
    Liedl, R., Netzer, N. and Reitberger, H., Eine Methods zur Berechnung von einparametrigen Untergruppen ohne Verwendung des Logarithmus (A method for calculation of one-parameter subgroups without using logarithm). Österreich. Akad. Wiss., Math.-Natur. K1. Sitzungsberg. 11 (1981), 273–284.Google Scholar
  56. [Lied], Netzer, Reitberger 82]
    Liedl, R., Netzer, N. and Reitberger, H., Über eine Methode zur Auffindung stetiger Iterationen in Lie-Gruppen (On a method of finding continuous iteration in Lie groups). Aequationes Math. 24 (1982), 19–32.MathSciNetzbMATHCrossRefGoogle Scholar
  57. [Liedl et al. 85]
    Liedl, R., Reich, L. and Targonski, Gy. (eds), Iteration Theory and its functional equations (Proceedings, Schloss Hofen 1984). Springer Lecture Notes in Mathematics Nr. 1163.Google Scholar
  58. [Mandelbrot 82]
    Mandelbrot, B. B., The fractal geometry of nature. W.H. Freeman, 1982.Google Scholar
  59. [Miller 92]
    Miller, J. B., Square root of uppertriangular matrices. [Analysis Paper No. 75], Dept. of Math., Monash University, Clayton, Vic., Australia, 1991.Google Scholar
  60. [Mira 79]
    Mira, C., Frontière floue séparant des domaines d’attraction de deux attracteurs (Vague boundaries separating the domains of attraction of two attractors). C. R. Acad. Sci. Paris 299 (1979), A591 - A594.MathSciNetGoogle Scholar
  61. [Mira, Müllenbach 83]
    Mira, C. and Müllenbach, S., Sur l’itération fractionnaire d’un endomorphisme quasratique (On fractional iteration of a quadratic endomorphism). C. R. Acad. S.i. Paris Sér. I. Math. 297 (1983), 369–372.zbMATHGoogle Scholar
  62. [Mira et al. 91]
    Mira, C., Netzer, N., Simó, C. and Targonski, GY. (eds), Proceedings of ECIT 89, European Conference on Iteration Theory, Batschu ns, Austria, 10–16 Sept. 1989. World Scientific, Singapore, 1991.Google Scholar
  63. [Netzer 82]
    Netzer, N., On the convergence of iterated pilgerschritt transforms. Zeszyty Nauk. Uniw. Jagiellon. Prace Mat. 23 (1982), 91–98.MathSciNetGoogle Scholar
  64. [Netzer, 92]
    Netzer, N., The convergence of fast Pilgerschritt transformation. In [Förg-Rob et al. 92].Google Scholar
  65. [Netzer, Liedl 91]
    Netzer, N. and Liedl, R., Fast Pilgerschritt transformation. In [Mira et al. 91], pp. 279–293.Google Scholar
  66. [Netzer, Reitberger 82]
    Netzer, N. and Reitberger, H., On the convergence of Pilgerschritt transformations in nilpotent Lie groups. Publ. Math. Debrecen 29 (1982), 309–314.MathSciNetzbMATHGoogle Scholar
  67. [Neuman 82]
    Neuman, F., Simultaneous solutions of a system of Abel equations and differential equations with several derivations. Czechoslovak Math. J. 32 (1982) 488–494.MathSciNetGoogle Scholar
  68. [Neuman 89]
    Neuman, F., On iteration groups of certain functions. Arch. Math. (Brno) 25 (1989), 185–194.MathSciNetzbMATHGoogle Scholar
  69. [Von Neumann 66]
    Von Neumann, J., Theory of self-reproducing automata. University of Illinois, Urbana-London, 1966.Google Scholar
  70. [Peitgen, Richter 86]
    Peitgen, H. O. and Richter, P. H., The beauty of fractals. Springer, Berlin, 1986.zbMATHGoogle Scholar
  71. [Peschl, Reich 71]
    Peschl, E. and Reich, L., Eine Linearisierung kontrahierender biholomorpher Abbildungen und damit zusammenhängender analytischer Differentialgleichungssysteme (A linearization method for contractive biholomorphic maps and for related systems of analytic differential equations). Monatsh. Math. 75 (1971),153–162.Google Scholar
  72. [Reich 71]
    Reich, L., Über analytische Iteration linearer und kontrahierender biholomorpher Abbildungen (On analytic iteration of linear and contractive biholomorphic mappings). [Bericht Nr. 42] Ges. Math. Datenverarb., Bonn, 1971.Google Scholar
  73. [Reich 79]
    Reich, L. (with the participation of J. Schwaiger), Analytische und fraktionelle Iteration formal-biholomorpher Abbildungen (Analytic and fractional iteration of formal biholomorphic maps). In Jahrbuch Überblicke Mathematik 1979, Bibliographisches Institut, Mannheim, 1979, pp. 123–144.Google Scholar
  74. [Reich 85]
    Reich, L., On a differential equation arising in iteration theory in rings of formal power series in one variable. In [Lied] et al. 85], pp. 135–148.Google Scholar
  75. [Reich 88]
    Reich, L., On families of commuting formal power series. In Selected topics in functional equations [Grazer Math. Bericht Nr. 294] Math-Stat. Sekkt. Forsch Ges. Joanneum, Graz, 1988, pp. 1–18.Google Scholar
  76. [Reich 89]
    Reich, L., Die Differentialgleichungen von Aczél-Jabotinsky, von Briot–Bouquet und maximale Familien vertauschbarer Potenzreihen (The differential equations of Aczél-Jabotinsky, of Briot -Bouquet and maximal families of commuting power series). In Complex methods on partial differential equations. [Math. Res. Vol. 53]. Akademie Verlag, Berlin, 1989, pp. 137–150.Google Scholar
  77. [Reich 91]
    Reich, L., On the embedding problem for formal power series with respect to the Aczél-Jabotinsky equations. In [Mira et al. 91], pp. 294–304.Google Scholar
  78. [Reich 92]
    Reich, L., On the local distribution of iterable power series transformation in one indeterminate. In: Functional analysis III, Proc. Postgrad School and Conf., Dubrovnik, Oct. 29-Nov. 2 (D. Brutkovic et al. eds). [Aarhus Univ. Various Publications Series Nr. 40], Univ., Aarhus, 1992.Google Scholar
  79. [Reich, 93]
    Reich, L., On power series transformations in one indeterminate having iterative roots of a given order and with given multiplier. In [Lampreia et al. 93], pp. 210–216.Google Scholar
  80. [Reich, Schwaiger 80]
    Reich, L. and Schwaiger J., Linearisierung formal-biholomorpher Abbildungen und Iterationsprobleme. Aequationes Math. 20 (1980), 224–243.MathSciNetzbMATHCrossRefGoogle Scholar
  81. [Riggert 75]
    Riggert, G., n-te iterative Wurzeln von beliebigen Abbildungen (n-th iterative roots of arbitrary sets). In Report of the 1975 International Symposium on Functional Equations. Aequationes Math. 15 (1977), 288.Google Scholar
  82. [Robert 86]
    Robert, F., Discrete iterations. Springer, Berlin, 1986.zbMATHCrossRefGoogle Scholar
  83. [Schleiermacher 93]
    Schleiermacher, A., On a theorem of Marc Krasner about invariant relations. In [Lampreia et al. 93], pp. 230–240.Google Scholar
  84. [Schwaiger 89]
    Schwaiger, J., Phantom roots and phantom iterates of formal power series in one variable. In [Alsina et al. 89], pp. 313–323.Google Scholar
  85. [Schwaiger 91]
    Schwaiger, J., On polynomials having different types of roots. In [Mira et al. 91], pp. 315–319.Google Scholar
  86. [Schwaizer, Sklar 88]
    Schweizer, B. and Sklar, A., Invariants and equivalence classes of polynomials under linear conjugacy. In Contributions to general algebra, No. 6. Hölder-Pinchler-Tempsky, Vienna and Teubner, Stuttgart, 1988.Google Scholar
  87. [Schwaizer, Sklar 90]
    Schweizer, B. and Sklar, A., The baker’s transformation is not embeddable. Found. of Phys. 20 (1990), 873–897.MathSciNetCrossRefGoogle Scholar
  88. [Simon 93]
    Simon, K., Hausdorff dimensions for certain near-hyperbolic maps. In [Lampreia et al. 93], pp. 253–261.Google Scholar
  89. [Sklar 69]
    Sklar, A., Canonical decompositions, stable functions, and fractional iterates. Aequationes Math. 3 (1969), 118–129.MathSciNetzbMATHCrossRefGoogle Scholar
  90. [Sklar 87]
    Sklar, A., The structure of one-dimensional flows with continuous trajectories. Rad. Mat. 3 (1987), 111–142.MathSciNetzbMATHGoogle Scholar
  91. [Skornjakov 77]
    Skornjakov, L. A., Unars. In Universal algebra. [Coll. Mat. Soc. Janos Bolyai 29], J. Bolyai Math. Soc. Budapest, 1977, pp. 735–743.Google Scholar
  92. [Smajdor 85]
    Smajdor, A., Iteration of multi-valued functions. [Prace Nauk. Uniw. Sl4sk. Katowic. No. 759], Silesian Univ. Katowice, 1985.Google Scholar
  93. [Smajdor 89]
    Smajdor, A., One-parameter families of set-valued contractions. In [Alsina et al. 89].Google Scholar
  94. [Smajdor 93]
    Smajdor, A., Almost-everywhere set-valued semigroups. In [Lampreia et al. 93], pp. 262–272.Google Scholar
  95. [Smital 88]
    Smital, J., On functions and functional equations. Adam Hilger, Bristol-Philadelphia, 1988.zbMATHGoogle Scholar
  96. [Snowden, Howie 82]
    Snowden, M. and Howie, J. M., Square roots in finite full transformation semigroups. Glasgow Math. J. 23 (1982), 137–149.MathSciNetzbMATHGoogle Scholar
  97. [Targonski 67]
    Targonski, GY., Seminar on functional operators and equations. [Springer Lecture Notes in Mathematics, No. 33], Springer, Berlin, 1967.Google Scholar
  98. [Targonski 81]
    Targonski, GY., Topics in iteration theory. Vandenhoeck & Ruprecht, Göttingen-Zürich, 1981.zbMATHGoogle Scholar
  99. [Targonski 84]
    Targonski, GY., New directions and open problems in iteration theory. [Grazer Math. Bericht No. 229], Math. Stat. Sekt. Forschungszentrum, Graz, 1984.Google Scholar
  100. [Targonski 841]
    Targonski, GY., Phantom iterates of continuous functions. In [Liedl et al. 85], pp. 196–202.Google Scholar
  101. [Targonski 89]
    Targonski, GY., Iteration theory and functional analysis. In [Alsina et al. 89], pp. 74–93.Google Scholar
  102. [Targonski 90]
    Targonski, GY., On composition operators. Zeszyty Nauk. Politechn. Sl4sk. Ser. Mat.-fiz. 64 (1990).Google Scholar
  103. [Targonski 91]
    Targonski, GY., Problem 25, In Report of the 27th ISFE, Poland 1989. Aequationes Math. 39 (1990), 313–314.Google Scholar
  104. [Targonski, 93]
    Targonski, GY., On a class of phantom fractional iterates. In [Lampreia et al. 93], pp. 295–301.Google Scholar
  105. [Targonski, 94]
    Targonski, GY., Phantom iterates and Liedl’s Pilgerschritt transformation. In [Förg-Rob et al. 94].Google Scholar
  106. [Targonski, Zdun 85]
    Targonski, GY. and Zdun, M. C., Generators and co-generators of substitution semigroups. Ann. Math.,Sil. 1 (13) (1985), 169–174.Google Scholar
  107. [Targonski, Zdun 87]
    Targonski, GY. and ZDUN, M. C., Substitution operators on LP-spaces and their semigroups. [Grazer Math. Bericht No. 283], Math.-Stat. Sekt. Forsch. Ges. Joanneum, Graz, 1987.Google Scholar
  108. [Thibault 89]
    Thibault, R., Some results obtained in Toulouse on dynamical systems. In [Alsina et al. 89], pp. 94–112.Google Scholar
  109. [Ushiki 86]
    Ushiki, Sh., Chaotic Phenomena and Fractal Objects in Numerical Analysis. In: Nishida, T. et al. (eds), Patterns and waves—qualitative analysis of nonlinear differential equations. [Stud. Math. Appl.], North Holland, Amsterdam, 1986, pp. 221–258.CrossRefGoogle Scholar
  110. [Wagon 85]
    Wagon, S., The Collatz problem. Math. Intelligencer 7 (1985), 72–76.MathSciNetzbMATHCrossRefGoogle Scholar
  111. [Weitkämper 85]
    Weitkämper, J., Embeddings in iteration groups and semigroups with nontrivial units. Stochastica 7 (1983), 175–195.MathSciNetzbMATHGoogle Scholar
  112. [Whitley 83]
    Whitley, D., Discrete dynamical systems in dimensions one and two. Bull. London Math. Soc. 15 (1983), 177–217.MathSciNetzbMATHCrossRefGoogle Scholar
  113. [Zdun 79]
    Zdun, M. C., Continuous and differentiable iteration semigroups. [Prace Nauk. Uniw. Sl4sk. Katowic. No. 308], Silesian Univ., Katowice, 1979.Google Scholar
  114. [Zdun 85]
    Zdun, M. C., On embedding of the circle in a continuous flow in [Lied) et al. 85], pp. 218–231.Google Scholar
  115. [Zdun 851]
    Zdun, M. C., Regular fractional iteration. Aequationes Math. 28 (1985), 73–79.MathSciNetzbMATHCrossRefGoogle Scholar
  116. [Zdun 88]
    Zdun, M. C., Note on commutable functions. Aequationes Math. 36 (1988), 153–164.MathSciNetzbMATHCrossRefGoogle Scholar
  117. [Zdun 89]
    Zdun, M. C., On continuity of iteration semigroups on metric spaces. Annal. Soc. Math. Polon. 29 (1989), 113–116.MathSciNetzbMATHGoogle Scholar
  118. [Zdun 891]
    Zdun, M. C., On C’ iteration groups. In [Alsina et al. 89], pp. 373–381.Google Scholar
  119. [Zdun 892]
    Zdun, M. C., On simultaneous Abel equations. Aequationes Math. 38 (1989), 163–177.MathSciNetzbMATHCrossRefGoogle Scholar
  120. [Zdun 90]
    Zdun, M. C., On quasi-continuous iteration semigroups and groups of real functions. Colloq. Math. 58 (1990), 281–289.MathSciNetzbMATHGoogle Scholar
  121. [Zdun 91]
    Zdun, M. C., The structure of iteration groups of continuous functions. Aequationes Math. 46 (1993), 19–37.MathSciNetzbMATHCrossRefGoogle Scholar
  122. [Zdun 911]
    Zdun, M. C., On continuous iteration groups of fixed point free mappings in R n space. In [Mira et al. 91], pp. 362–368.Google Scholar
  123. [Zdun 93]
    Zdun, M. C., Some remarks on the iterates of commuting functions. In [Lampreia et al. 93], pp. 336–342.Google Scholar

Copyright information

© Birkhäuser Verlag Basel 1995

Authors and Affiliations

  1. 1.Fachbereich MathematikUniversität MarburgMarburgGermany

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