Spectral theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps

Keller G, Nowicki T (1992)

Publication Type: Journal article, Original article

Publication year: 1992

Journal

Communications in Mathematical Physics Springer Verlag (Germany)

Book Volume: 149

Pages Range: 31--69

Journal Issue: 1

URI: http://projecteuclid.org/euclid.cmp/1104251138

DOI: 10.1007/BF02096623

Abstract

We study unimodal interval mapsT with negative Schwarzian derivative satisfying the Collet-Eckmann condition |DT n (Tc)|≧Kλ c n for some constantsK>0 and λc>1 (c is the critical point ofT). We prove exponential mixing properties of the unique invariant probability density ofT, describe the long term behaviour of typical (in the sense of Lebesgue measure) trajectories by Central Limit and Large Deviations Theorems for partial sum processes of the formSn=Σn−1i=0f(Tix)

, and study the distribution of “typical” periodic orbits, also in the sense of a Central Limit Theorem and a Large Deviations Theorem.

This is achieved by proving quasicompactness of the Perron Frobenius operator and of similar transfer operators for the Markov extension ofT and relating the isolated eigenvalues of these operators to the poles of the corresponding Ruelle zeta functions.

Authors with CRIS profile

Gerhard Keller Professur für Angewandte Mathematik (Angewandte Analysis)

How to cite

APA:

Keller, G., & Nowicki, T. (1992). Spectral theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps. Communications in Mathematical Physics, 149(1), 31--69. https://doi.org/10.1007/BF02096623

MLA:

Keller, Gerhard, and Tomasz Nowicki. "Spectral theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps." Communications in Mathematical Physics 149.1 (1992): 31--69.

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