Skip to main content
SpringerLink
Log in

Y

  • Chapter
Encyclopaedia of Mathematics

Part of the book series: Encyclopaedia of Mathematics ((ENMA,volume 9))

  • 591 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anosov, D.V.: ‘Roughness of geodesic flows on compact Riemannian manifolds of negative curvature’, Soviet Math. Dokl. 3 (1962), 1068–1069. (Dokl. Akad. Nauk SSSR 145, no. 4 (1962), 707–709)

    MATH  Google Scholar 

  2. Anosov, D.V.: ‘Ergodic properties of geodesic flows on closed Riemannian manifolds of negative curvature’, Soviet Math. Dokl. 4 (1963), 1153–1156. (Dokl. Akad. Nauk SSSR 151, no. 6 (1963), 1250–1252)

    MATH  Google Scholar 

  3. Anosov, D.V.: ‘Geodesic flows on closed Riemann manifolds of negative curvature’, Proc. Steklov Inst. Math. 90 (1969). (Trudy Mat. Inst. Steklov. 90 (1967))

    Google Scholar 

  4. Anosov, D.V.: ‘Some smooth ergodic systems’, Russian Math. Surveys 22, no. 5 (1967), 103–167. (Uspekhi Mat. Nauk. 22, no. 5 (1967), 107–172)

    Article  MathSciNet  Google Scholar 

  5. Sinaĭ, Ya.G.: ‘Gibbs measures in ergodic theory’, Russian Math. Surveys 27, no. 4 (1972), 21–64. (Uspekhi Mat. Nauk.)

    Article  MATH  Google Scholar 

  6. Bowen, R.: Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Springer, 1975.

    MATH  Google Scholar 

  7. Katok, A.B., Sinai, Ya.G. and Stepin, A.M.: ‘Theory of dynamical systems and general transformation groups with invariant measure’, J. Soviet Math. 7 (1977), 974–1065. (Itogi Nauk. i Tekhn. Mat. Anal. 13 (1975), 129–262)

    Article  Google Scholar 

  8. Adler, R.L. and Weiss, B.: ‘Similarity of automorphisms of the torus’, Mem. Amer. Math. Soc. 98 (1970).

    Google Scholar 

  9. Sinaĭ, Ya.G.: ‘Construction of Markov partitions’, Fund. Anal. Appl. 2 (1968), 70–80. (Funkts. Anal, i Prilozh. 2 (1968), 64–89)

    Google Scholar 

  10. Franks, J.M. and Williams, B.: ‘Anomalous Anosov flows’, in Z. Nitecki and C. Robinson (eds.): Global Theory of Dynamical Systems (Proc. Evanston, 1969), Lecture notes in math., Vol. 819, Springer, 1980, pp. 158–174.

    Chapter  Google Scholar 

  11. Hirsch, M.W.: ‘Anosov maps, polycyclic groups and homology’, Topology 10, no. 3 (1971), 177–183.

    Article  MathSciNet  MATH  Google Scholar 

  12. Shiraiwa, K.: ‘Manifolds which do not admit Anosov dif-feomorphisms’, Nagoya Math. J. 49 (1973), 111–115.

    MathSciNet  MATH  Google Scholar 

  13. Franks, J.: ‘Anosov difisomorphisms’, in Global Analysis, Proc. Sympos. Pure Math., Vol. 14, Amer. Math. Soc, 1970, pp. 61–93.

    Google Scholar 

  14. Newhouse, S.E.: ‘On codimension one Anosov diffeomor-phisms’, Amer. J. Math. 92 (1970), 761–770.

    Article  MathSciNet  MATH  Google Scholar 

  15. Manning, A.: ‘There are no new Anosov diffeomorphisms on tori’, Amer. J. Math. 96 (1974), 422–429.

    Article  MathSciNet  MATH  Google Scholar 

  16. Verjovsky, A.: ‘Codimension one Anosov flows’, Bolet. Soc. Mat. Mexicana 19, no. 2 (1974), 49–77.

    MathSciNet  MATH  Google Scholar 

  17. Fahti, A. and Laudenbach, F.: ‘Les feuilletages mesurés’, Astérisque 66–67 (1979), 71–126.

    Google Scholar 

  18. Fahti, A. and Laudenbach, F.: ‘Comment Thurston compactifie l’espace de Teichmüller’, Astérisque 66–67 (1979), 139–158.

    Google Scholar 

  19. Fahti, A. and Poénaru, V.: ‘Theorème d’unicité des difféomorphismes pseudo-Anosov’, Astérisque 66–67 (1979), 225–242.

    Google Scholar 

  20. Solodov, V.V.: ‘Topological questions in the theory of dynamical systems’, Russian Math. Surveys 46, no. 4 (1991), 107–130. (Uspekhi Mat. Nauk 46, no. 4 (1991), 91–114)

    Article  MathSciNet  Google Scholar 

  21. Adachi, T.: ‘Distribution of closed orbits with a pre-assigned homology class in a negatively curved manifold’, Nagoya Math. J. 110 (1988), 1–14.

    Article  MathSciNet  MATH  Google Scholar 

  22. Bowen, R.: On axiom A diffeomorphisms, Amer. Math. Soc., 1978.

    MATH  Google Scholar 

  23. Eberlein, P.: ‘When is a geodesic flow Anosov type?’, J. Differential Geom. 8 (1973), 437–463.

    MathSciNet  MATH  Google Scholar 

  24. Plante, J.F.: ‘Homology of closed orbits of Anosov flows’, Proc. Amer. Math. Soc. 37 (1973), 297–300.

    Article  MathSciNet  MATH  Google Scholar 

  25. Shub, M.: Global stability of dynamical systems, Springer, 1986.

    Google Scholar 

  26. Palis, J. and De Melo, W.: Geometric theory of dynamical systems, Springer, 1982.

    Book  MATH  Google Scholar 

  27. Smale, S.: ‘Differentiate dynamical systems’, Bull. Amer. Math. Soc. 73 (1967), 747–817.

    Article  MathSciNet  MATH  Google Scholar 

  28. Jimbo, M. (ed.): Yang—Baxter equation in integrable systems, World Scientific, 1990.

    MATH  Google Scholar 

  29. Zamolodchikov, A.B. and Zamolodchikov, Al.B.: ‘Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models’, Ann. Physics 120 (1979), 253–291. (Reprinted in [A1], 82–120.).

    Article  MathSciNet  Google Scholar 

  30. Baxter, R.J.: ‘Solvable eight-vertex model on an arbitrary planar lattice’, Phil. Trans. Royal Soc. London 289 (1978), 315–346. (Reprinted in [A1], 50–81.).

    MathSciNet  Google Scholar 

  31. Baxter, R.J.: Exactly solved models in statistical mechanics, Acad. Press, 1982.

    MATH  Google Scholar 

  32. McGuire, J.B.: ‘Study of exactly solvable one-dimensional N-body problems’, J. Math. Physics 5 (1964), 622–636.

    Article  MathSciNet  MATH  Google Scholar 

  33. Yang, C.N.: ‘Some exact results for the many-body problemin one dimension with delta-function interaction’, Phys. Rev. Lett. 19(1967), 1312–1314.

    Article  MathSciNet  MATH  Google Scholar 

  34. Onsager, L.: ‘Crystal lattices I. A two dimensional model with an order-disorder transition’, Phys. Rev. 65 (1944), 117–149.

    Article  MathSciNet  MATH  Google Scholar 

  35. Faddeev, L.D.: ‘Integrable models in (1 +1)-dimensional quantum field theory’, in Les Houches, Vol. Session 39, Elsevier, 1982, pp. 563–608.

    Google Scholar 

  36. Yang, C.N. and Ge, M.L. (eds.): Braid group, knot theory and statistical mechanics, World Scientific, 1989.

    MATH  Google Scholar 

  37. Jimbo, M.: ‘Introduction to the Yang-Baxter equation’, in M. Jimbo (ed.): Yang-Baxter equation in integrable systems, World Scientific, 1990, pp. 111–134.

    Google Scholar 

  38. Hazewinkel, M.: ‘Introductory recommendations for the study of Hopf algebras in mathematics and physics’, CWI Quarterly 4 (1991), 3–26.

    MathSciNet  MATH  Google Scholar 

  39. Semenov-Tyan-Shanskiĭ, M.A.: ‘What is a classical r-matrix’, Funct. Anal. Appl. 17 (1984), 259–272. (Reprinted in [A1], 226–2242.). (Funkts. Anal. Prilozh. 17, no. 4 (1983), 17–33)

    Article  Google Scholar 

  40. Belavin, A.A. and Drinfel’d, V.G.: ‘Solutions of the classical Yang —Baxter equation for simple Lie algebras’, Funct. Anal. Appl. 16 (1983), 159–180. (Reprinted in [A1], 200–221.). (Funkts. Anal. Prilozhe 16, no. 3 (1982), 1–29)

    Article  Google Scholar 

  41. Lyubashenko, V.V.: ‘Hopf algebras and vector symmetries’, Russ. Math. Surveys 41 (1986), 153–154. (Uspekhi Mat. Nauk 41 (1986), 185–186)

    Article  MathSciNet  MATH  Google Scholar 

  42. Faddeev, L.D., Reshetikhin, N.Yu. and Takhtadzhyan, L.A.: ‘Quantization of Lie groups and Lie algebras’, Algebra and Analysis 1 (1989), 178–206 (in Russian).

    MathSciNet  Google Scholar 

  43. Manin, Yu.I.: ‘Gauge fields and holomorphic geometry’, J. Soviet Math. 21, no. 4 (1983), 465–507. (Itogi Nauk. i Tekhn. Sovr. Probl. Mat. 17 (1981), 3–55)

    Article  MATH  Google Scholar 

  44. Shvarts, A.S.: ‘Elliptic operators in quantum field theory’, J. Soviet Math. 21, no. 4 (1983), 551–601. (Itogi Nauk. i Tekhn. Sovr. Probl. Mat. 17 (1981), 113–173)

    Article  MATH  Google Scholar 

  45. Atiyah, M.F., Hitchin, N.J. and Singer, I.M.: ‘Self-duality in four-dimensional Riemannian geometry’, Proc. Roy. Soc. London A 362 (1978), 425–461.

    Article  MathSciNet  MATH  Google Scholar 

  46. Popov, D.A. and Daĭkhin, L.I.: ‘Einstein spaces, and Yang-Mills fields’, Dokl. Akad. Nauk SSSR 225, no. 4 (1975), 790–793 (in Russian).

    MathSciNet  Google Scholar 

  47. Bourguignon, J.: Proc. Nat. Acad. Sci. USA 76, no. 4 (1979), 1550–1553.

    Article  MathSciNet  MATH  Google Scholar 

  48. Konopleva, N.P. and Popov, V.N.: Gauge fields, Horwood, 1981 (translated from the Russian).

    MATH  Google Scholar 

  49. Yang, C.N. and Mills, R.L.: ‘Conservation of isotopic spin and isotopic gauge invariance’, Phys. Rev. 96, no. 1 (1954), 191–195.

    Article  MathSciNet  Google Scholar 

  50. Geometrical ideas in physics, Moscow, 1983 (in Russian; translated from the English).

    Google Scholar 

  51. Freed, D.S. and Uhlenbeck, K.K.: Instantons and four manifolds, Springer, 1984.

    Book  MATH  Google Scholar 

  52. Manin, Yu.I.: Gauge field theory and complex geometry, Springer, 1988.

    MATH  Google Scholar 

  53. Albeverio, S., Paycha, S. and Scarlatti, S.: ‘A short overview of mathematical approaches to functional integration’, in Z. Haba and J. Sobczyk (eds.): Functional Integration, Geometry and Strings, Birkhäuser, 1989, pp. 230–276.

    Google Scholar 

  54. DeWitt, B.S.: Dynamical theory of groups and fields, Gordon & Breach, 1964.

    Google Scholar 

  55. Cheng, T.-P. and Li, L.-F.: Gauge theory of elementary particle physics, Clarendon Press, 1984.

    Google Scholar 

  56. Nélipa, N.: Physique des particules élémentaires, Mir.

    Google Scholar 

  57. Atiyah, M.F.: Geometry of Yang—Mills fields, Scuola Norm. Sup. Pisa, 1979.

    MATH  Google Scholar 

  58. Doubrovine, B. [B. Dubrovin], Novikov, S. and Fomenko, A.: Contemporary geometry, Springer, 1990 (translated from the Russian).

    Google Scholar 

  59. Lawson, B. and Michelsohn, M.-L.: Spin geometry, Princeton Univ. Press, 1989.

    MATH  Google Scholar 

  60. Bleecker, D.: Gauge theory and variational principles, Addison-Wesley, 1981.

    MATH  Google Scholar 

  61. Yates, J.: Trans. Roy. Stat. Soc. 1 (1934), 217.

    Google Scholar 

  62. Cramer, H.: Mathematical methods of statistics, Princeton Univ. Press, 1946.

    MATH  Google Scholar 

  63. Hager, A.W. and Robertson, L.C.: ‘Representing and ringifying a Riesz space’, in Symp. Math. INDAM, Vol. 21, Acad. Press, 1977, pp. 411–432.

    Google Scholar 

  64. Luxemburg, W.A.J. and Zaanen, A.C.: Riesz spaces, 1, North-Holland, 1971.

    MATH  Google Scholar 

  65. Jonge, E. de and Rooy, A.C.M. van: Introduction to Riesz spaces, Mathematical Centre, Amsterdam, 1977.

    MATH  Google Scholar 

  66. Young, W.H.: ‘On the convergence of the derived series of Fourier series’, Proc. London Math. Soc. 17 (1916), 195–236.

    Article  Google Scholar 

  67. Bary, N.K. [N.K. Bari]: A treatise on trigonometric series, Pergamon, 1964 (translated from the Russian).

    MATH  Google Scholar 

  68. Zygmund, A.: Trigonometric series, 1–2, Cambridge Univ. Press, 1988.

    MATH  Google Scholar 

  69. Young, A.: ‘On quantitative substitutional analysis’, Proc. London Math. Soc. 33 (1901), 97–146.

    Article  MATH  Google Scholar 

  70. Young, A.: ‘On quantitative substitutional analysis’, Proc. London Math. Soc. 34 (1902), 361–397.

    Article  MATH  Google Scholar 

  71. Kerber, A. and James, G.D.: The representation theory of the symmetric group, Addison-Wesley, 1981.

    MATH  Google Scholar 

  72. Kerber, A.: Algebraic combinatorics via finite group actions, B.I. Wissenschaftsverlag, 1991.

    MATH  Google Scholar 

  73. Andrews, G.E.: The theory of partitions, Addison-Wesley, 1976.

    MATH  Google Scholar 

  74. Macdonald, I.G.: Symmetric functions and Hall polynomials, Clarendon Press, 1979.

    MATH  Google Scholar 

  75. James, G.D.: The representation theory of the symmetric groups, Springer, 1978, p. 13.

    MATH  Google Scholar 

  76. Kerber, A.: Representations of permutation groups, I, Springer, 1971, p. 17.

    MATH  Google Scholar 

  77. Knuth, D.: The art of computer programming, 3, Addison-Wesley, 1973.

    Google Scholar 

Download references

Authors
  1. M. Hazewinkel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

M. Hazewinkel

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Kluwer Academic Publishers

About this chapter

Cite this chapter

Hazewinkel, M. (1993). Y. In: Hazewinkel, M. (eds) Encyclopaedia of Mathematics. Encyclopaedia of Mathematics, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-1233-6_6

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-1233-6_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-8238-1

  • Online ISBN: 978-94-015-1233-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation