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Progress of iteration theory since 1981

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Abstract

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.

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References

  1. Aczél, J., Einige aus Funktionalgleichungen zweier Veränderlichen ableitbare Differentialgeichungen. Acta Sci. Math. (Szeged) 13 (1949), 179–189.

    Google Scholar 

  2. Aczél, J., Remarks on a problem of Gy. Targonski. Report of the 27th ISFE, Poland 1989. Aequationes Math. 39 (1990), 314–315.

    Article  Google Scholar 

  3. Aczél, J., and Gronau, D., Some differential equations related to iteration theory. Canad. J. Math. 40 (1988), 695–717.

    Article  MathSciNet  MATH  Google Scholar 

  4. 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, 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. Alseda, LL., Llibre, J. and Misiurewicz, M., Combinatorial dynamics and entropy in dimension one. World Scientific, Singapore, 1992.

    Google Scholar 

  7. 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, M., Fractals everywhere. Academic Press, New York, 1988.

    MATH  Google Scholar 

  9. Bartels, A., Über iterative Phantomwurzeln von Abbildungen (On iterative phantom roots of mappings). Diploma ( M.Sc.) Thesis, Universität Marburg, 1991.

    Google Scholar 

  10. Blanchard, P., Complex analytic dynamics of the Riemann sphere. Bull. Amer. Math. Soc. 11 (1984), 95–141.

    Article  MathSciNet  Google 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.

    MATH  Google Scholar 

  12. Böttcher, A. and Heidler, H., Algebraic composition operators. Integral Equations Operator Theory 15 (1992), 390–411.

    Article  Google Scholar 

  13. 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, C., Sur les transmutations (On transmutations). Bull. Soc. Math. France 25 (1897), 132–140.

    MathSciNet  MATH  Google Scholar 

  15. Burkart, U., Zur Charakterisierung diskreter dynamischer Systeme (On characterization of discrete dynamical systems). Ph.D. Thesis, Universität Marburg, 1982.

    Google Scholar 

  16. Cap, C. H., Two approaches to the iteration problem of diffeomorphisms. In [Alsina et al. 89], pp. 139–144.

    Google Scholar 

  17. Cap, C. H., Solving Abel, Jabotinsky and inverse ODE problems. In [Mira et al. 91], pp. 19–28.

    Google Scholar 

  18. 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.

    MathSciNet  MATH  Google Scholar 

  19. Collet, P. and Eckmann, J. P., Iterated maps on the interval as dynamical systems. Birkhäuser, Boston, 1980.

    MATH  Google Scholar 

  20. Deslauriers, G. and Dubuc, S., Continuous iterative iteration processes. In [Mira et al. 91], pp. 71–78.

    Google Scholar 

  21. 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. Dusuc, S., Functional equations connected with peculiar curves. In [Liedl et al. 85], pp. 33–40.

    Google Scholar 

  23. Ecalle, J., Les fonctions résurgents (On resurgent functions), vol. 1, 2, [Publ. Math. Orsay], Univ. d’Orsay, Orsay, 1981.

    Google Scholar 

  24. Ecalle, J., Iteration and analytic classification of local diffeomorphisms of C’. In [Lied(et al. 85], pp. 41–48.

    Google Scholar 

  25. Farmer, D. et al. (eds), Cellular automata. North Holland, Amsterdam, 1985.

    Google Scholar 

  26. Ferber, R., Zelluläre Automaten als dynamische Systeme (Cellular automata as dynamical systems). Diploma ( M.Sc.) Thesis, Universität Marburg, 1985.

    Google Scholar 

  27. 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, R., Cellular automata are the continuous self-mappings of configuration spaces. In [Mira et ai. 91], pp. 79–85.

    Google Scholar 

  29. 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, W., The Pilgerschritt transform in Lie algebras. In [Lied(et al. 85], pp. 59–71.

    Google Scholar 

  31. Förg-Rob, W., Some results on the Pilgerschritt transform. In [Alsina et al. 89], pp. 198–204.

    Google Scholar 

  32. 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, 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, D., Conjectures. Math. Intelligencer 13 (1991), 53–55.

    Article  MathSciNet  Google Scholar 

  35. Gardner, M., Mathematical games. Scientific American, Oct. 1970 and Feb. 1971.

    Google Scholar 

  36. Gravi, R., Über die Orbitstruktur stetiger Abbildungen (On the orbit structure of continuous mappings.). Ph.D. Thesis, Universität Marburg, 1982.

    Google Scholar 

  37. Gravi, R., Compact orbits and periodicity. Nonlinear Anal. 8 (1984), 1473–1479.

    Article  MathSciNet  Google Scholar 

  38. Gronau, D., The Jabotinsky equations and the embedding problem. In [Mira et al. 91], pp. 138–148.

    Google Scholar 

  39. Gronau, D., On the structure of the solution of the Jabotinsky equations in Banach spaces. Zeitschr. Anal. Anw. 10 (1991), 335–343.

    MathSciNet  MATH  Google Scholar 

  40. Gumowski, I. and Mira, C., Dynamique chaotique (Chaotic dynam- ics). Cepadues Editions, Toulouse, 1980.

    Google Scholar 

  41. Gumowski, I. and Mira, C., Recurrences and discrete dynamic systems. [Springer Lecture Notes in Mathematics, Nr. 809], Springer, Berlin, 1980.

    Google Scholar 

  42. Isaacs, R., Iterates of fractional order. Canad. J. Math. 2 (1950), 409–416.

    Article  MathSciNet  MATH  Google Scholar 

  43. Jabotinsky, E., Iteration. Ph.D. Thesis, The Hebrew University, Jerusalem, 1955.

    Google Scholar 

  44. Jabotinsky, E., Analytic iteration. Trans. Amer. Math. Soc. 108 (1963), 457–477.

    Article  MathSciNet  MATH  Google Scholar 

  45. Krasner, M., Une géneralisation de la notion de corps (A generalization of the notion of field). J. M.th. Pures Appl. 17 (1938), 367–385.

    MATH  Google Scholar 

  46. Krause, G., Manuscript, 1988.

    Google Scholar 

  47. 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, J. C., The 3x + 1 problem and its generalizations. American Math. Monthly 92 (1985), 3–23.

    Article  MathSciNet  MATH  Google Scholar 

  49. Lampreia, J. P. and Sousa Ramos, J., Symbolic dynamics of trimodal maps. In [Mira et al. 91], pp. 184–193.

    Google Scholar 

  50. 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, H., Zellulare Automaten und Iterationstheorie (Cellular automata and iteration theory). Diploma ( M.Sc.) Thesis, Universität Marburg, 1992.

    Google Scholar 

  52. Liedl, R., Gruppenwertige Potenzreihen (Group valued power series). Anz. Österreich. Akad. Wiss. Math. Nat. K1. 1986, No. 5, 57–58.

    MathSciNet  Google Scholar 

  53. 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, 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. 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. 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.

    Article  MathSciNet  MATH  Google Scholar 

  57. 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, B. B., The fractal geometry of nature. W.H. Freeman, 1982.

    Google Scholar 

  59. 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, 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.

    MathSciNet  Google Scholar 

  61. 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.

    MATH  Google Scholar 

  62. 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, N., On the convergence of iterated pilgerschritt transforms. Zeszyty Nauk. Uniw. Jagiellon. Prace Mat. 23 (1982), 91–98.

    MathSciNet  Google Scholar 

  64. Netzer, N., The convergence of fast Pilgerschritt transformation. In [Förg-Rob et al. 92].

    Google Scholar 

  65. Netzer, N. and Liedl, R., Fast Pilgerschritt transformation. In [Mira et al. 91], pp. 279–293.

    Google Scholar 

  66. Netzer, N. and Reitberger, H., On the convergence of Pilgerschritt transformations in nilpotent Lie groups. Publ. Math. Debrecen 29 (1982), 309–314.

    MathSciNet  MATH  Google Scholar 

  67. Neuman, F., Simultaneous solutions of a system of Abel equations and differential equations with several derivations. Czechoslovak Math. J. 32 (1982) 488–494.

    MathSciNet  Google Scholar 

  68. Neuman, F., On iteration groups of certain functions. Arch. Math. (Brno) 25 (1989), 185–194.

    MathSciNet  MATH  Google Scholar 

  69. Von Neumann, J., Theory of self-reproducing automata. University of Illinois, Urbana-London, 1966.

    Google Scholar 

  70. Peitgen, H. O. and Richter, P. H., The beauty of fractals. Springer, Berlin, 1986.

    MATH  Google Scholar 

  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, 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, 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, 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, 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, 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, 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, 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, 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, L. and Schwaiger J., Linearisierung formal-biholomorpher Abbildungen und Iterationsprobleme. Aequationes Math. 20 (1980), 224–243.

    Article  MathSciNet  MATH  Google Scholar 

  81. 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, F., Discrete iterations. Springer, Berlin, 1986.

    Book  MATH  Google Scholar 

  83. Schleiermacher, A., On a theorem of Marc Krasner about invariant relations. In [Lampreia et al. 93], pp. 230–240.

    Google Scholar 

  84. 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, J., On polynomials having different types of roots. In [Mira et al. 91], pp. 315–319.

    Google Scholar 

  86. 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. Schweizer, B. and Sklar, A., The baker’s transformation is not embeddable. Found. of Phys. 20 (1990), 873–897.

    Article  MathSciNet  Google Scholar 

  88. Simon, K., Hausdorff dimensions for certain near-hyperbolic maps. In [Lampreia et al. 93], pp. 253–261.

    Google Scholar 

  89. Sklar, A., Canonical decompositions, stable functions, and fractional iterates. Aequationes Math. 3 (1969), 118–129.

    Article  MathSciNet  MATH  Google Scholar 

  90. Sklar, A., The structure of one-dimensional flows with continuous trajectories. Rad. Mat. 3 (1987), 111–142.

    MathSciNet  MATH  Google Scholar 

  91. 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, A., Iteration of multi-valued functions. [Prace Nauk. Uniw. Sl4sk. Katowic. No. 759], Silesian Univ. Katowice, 1985.

    Google Scholar 

  93. Smajdor, A., One-parameter families of set-valued contractions. In [Alsina et al. 89].

    Google Scholar 

  94. Smajdor, A., Almost-everywhere set-valued semigroups. In [Lampreia et al. 93], pp. 262–272.

    Google Scholar 

  95. Smital, J., On functions and functional equations. Adam Hilger, Bristol-Philadelphia, 1988.

    MATH  Google Scholar 

  96. Snowden, M. and Howie, J. M., Square roots in finite full transformation semigroups. Glasgow Math. J. 23 (1982), 137–149.

    MathSciNet  MATH  Google Scholar 

  97. Targonski, GY., Seminar on functional operators and equations. [Springer Lecture Notes in Mathematics, No. 33], Springer, Berlin, 1967.

    Google Scholar 

  98. Targonski, GY., Topics in iteration theory. Vandenhoeck & Ruprecht, Göttingen-Zürich, 1981.

    MATH  Google Scholar 

  99. 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, GY., Phantom iterates of continuous functions. In [Liedl et al. 85], pp. 196–202.

    Google Scholar 

  101. Targonski, GY., Iteration theory and functional analysis. In [Alsina et al. 89], pp. 74–93.

    Google Scholar 

  102. Targonski, GY., On composition operators. Zeszyty Nauk. Politechn. Sl4sk. Ser. Mat.-fiz. 64 (1990).

    Google Scholar 

  103. Targonski, GY., Problem 25, In Report of the 27th ISFE, Poland 1989. Aequationes Math. 39 (1990), 313–314.

    Google Scholar 

  104. Targonski, GY., On a class of phantom fractional iterates. In [Lampreia et al. 93], pp. 295–301.

    Google Scholar 

  105. Targonski, GY., Phantom iterates and Liedl’s Pilgerschritt transformation. In [Förg-Rob et al. 94].

    Google Scholar 

  106. 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, 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, R., Some results obtained in Toulouse on dynamical systems. In [Alsina et al. 89], pp. 94–112.

    Google Scholar 

  109. 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.

    Chapter  Google Scholar 

  110. Wagon, S., The Collatz problem. Math. Intelligencer 7 (1985), 72–76.

    Article  MathSciNet  MATH  Google Scholar 

  111. Weitkämper, J., Embeddings in iteration groups and semigroups with nontrivial units. Stochastica 7 (1983), 175–195.

    MathSciNet  MATH  Google Scholar 

  112. Whitley, D., Discrete dynamical systems in dimensions one and two. Bull. London Math. Soc. 15 (1983), 177–217.

    Article  MathSciNet  MATH  Google Scholar 

  113. Zdun, M. C., Continuous and differentiable iteration semigroups. [Prace Nauk. Uniw. Sl4sk. Katowic. No. 308], Silesian Univ., Katowice, 1979.

    Google Scholar 

  114. Zdun, M. C., On embedding of the circle in a continuous flow in [Lied) et al. 85], pp. 218–231.

    Google Scholar 

  115. Zdun, M. C., Regular fractional iteration. Aequationes Math. 28 (1985), 73–79.

    Article  MathSciNet  MATH  Google Scholar 

  116. Zdun, M. C., Note on commutable functions. Aequationes Math. 36 (1988), 153–164.

    Article  MathSciNet  MATH  Google Scholar 

  117. Zdun, M. C., On continuity of iteration semigroups on metric spaces. Annal. Soc. Math. Polon. 29 (1989), 113–116.

    MathSciNet  MATH  Google Scholar 

  118. Zdun, M. C., On C’ iteration groups. In [Alsina et al. 89], pp. 373–381.

    Google Scholar 

  119. Zdun, M. C., On simultaneous Abel equations. Aequationes Math. 38 (1989), 163–177.

    Article  MathSciNet  MATH  Google Scholar 

  120. Zdun, M. C., On quasi-continuous iteration semigroups and groups of real functions. Colloq. Math. 58 (1990), 281–289.

    MathSciNet  MATH  Google Scholar 

  121. Zdun, M. C., The structure of iteration groups of continuous functions. Aequationes Math. 46 (1993), 19–37.

    Article  MathSciNet  MATH  Google Scholar 

  122. 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, M. C., Some remarks on the iterates of commuting functions. In [Lampreia et al. 93], pp. 336–342.

    Google Scholar 

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Targonski, G. (1995). Progress of iteration theory since 1981. In: Aczél, J. (eds) Aggregating clones, colors, equations, iterates, numbers, and tiles. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9096-0_5

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