A note on dynamical zeta functions for S-unimodal maps

• Autorzy: Gerhard Keller
• Języki publikacji: EN

Abstrakty

EN

Let f be a nonrenormalizable S-unimodal map. We prove that f is a Collet-Eckmann map if its dynamical zeta function looks like that of a uniformly hyperbolic map.

Słowa kluczowe

EN

dynamical zeta function; Collet-Eckmann map

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2000
• Tom: 84/85
• Numer: 1
• Strony: 229-233

Daty

wydano

2000

otrzymano

1999-07-15

Twórcy

autor

Gerhard Keller

• Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstr. 1 1/2, D-91054 Erlangen, Germany

Bibliografia

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• [3] H. Bruin and G. Keller, Equilibrium states for S-unimodal maps, ibid. 18 (1998), 765-789.
• [4] G. Keller and T. Nowicki, Fibonacci maps re(al)visited, ibid. 15 (1995), 99-120.
• [5] W. de Melo and S. van Strien, One-Dimensional Dynamics, Springer, 1993.
• [6] T. Nowicki and D. Sands, Non-uniform hyperbolicity and universal bounds for S-unimodal maps, Invent. Math. 132 (1998), 633-680.
• [7] Y. Oono and Y. Takahashi, Chaos, external noise and Fredholm theory, Progr. Theor. Phys. 63 (1980), 1804-1807.
• [8] R. Remmert, Theory of Complex Functions, Grad. Texts in Math. 122, Springer, New York, 1991.
• [9] D. Ruelle, Analytic completion for dynamical zeta functions, Helv. Phys. Acta 66 (1993), 181-191.
• [10] Y. Takahashi, An ergodic-theoretical approach to the chaotic behaviour of dynamical systems, Publ. R.I.M.S. Kyoto Univ. 19 (1983), 1265-1282.