Download PDF - A note on dynamical zeta functions for S-unimodal mapsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

A note on dynamical zeta functions for S-unimodal maps

Authors 1

Affiliations

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

Abstract

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.

Keywords

ENG
dynamical zeta function, Collet-Eckmann map

Bibliography

  1. V. Baladi and G. Keller, Zeta-functions and transfer operators for piecewise monotone transformations, Comm. Math. Phys. 127 (1990), 459-478.
  2. V. Baladi, Periodic orbits and dynamical spectra, Ergodic Theory Dynam. Systems 18 (1998), 255-292.
  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.
Colloquium Mathematicum
2000/84/85/1
Export to PBN, Opens in new tab
Pages:
229-233
Main language of publication
English
Received
1999-07-15
Published
2000
Exact and natural sciences