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Entropy and periodic orbits for generic diffeomorphisms

Ruixin Chen
대한수학회 (The Korean Mathematical Society)|2013.05|대한수학회보 (Bulletin of the KMS)|제50권 제3호|pp. 727-730

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키워드

topological entropygeneric diffeomorphismgrowth rate of periodic orbits
주제분류수학

초록

We prove an inequality between topological entropy and asymptotical growth of periodic orbits for C1 generic diffeomorphisms.

Abstract

We prove an inequality between topological entropy and asymptotical growth of periodic orbits for C1 generic diffeomorphisms.

참고문헌 (7)

  1. C. Bonatti, "Perturbations of the derivative along periodic orbits", Ergodic Theory Dynam. Systems, 26(5), pp.1307~1337 (2006)
  2. R. Bowen, "Topological entropy and Axiom A", Proc. Symp. PureMath. A.M.S., Providence R.I., 14, pp.13~41 (1970)
  3. S. Hayashi, "Diffeomorphisms in F1(M) satisfy Axiom A", Ergodic Theory Dynam. Systems, 12(2), pp.233~253 (1992)
  4. A. Katok, "Lyapunov exponents, entropy and periodic orbits for diffeomorphisms", Inst. Hautes ´Etudes Sci. Publ. Math, (51), pp.137~173 (1980)
  5. I. Kupka, "Contributiona la th´eorie des champs generiques", Contrib. Differ. Equ, 2, pp.457~484 (1963)
  6. R. Mane, "An ergodic closing lemma", Ann. of Math, 116(3), pp.503~540 (1982)
  7. S. Smale, "Stable manifolds for differential equations and diffeomorphisms", Ann. Scuola Norm. Sup. Pisa, 17, pp.97~116 (1963)

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