Equilibrium states for S-unimodal maps

Bruin HP, Keller G (1998)

Publication Type: Journal article, Original article

Publication year: 1998

Journal

Ergodic Theory and Dynamical Systems Cambridge University Press (CUP)

Publisher: Cambridge University Press (CUP)

Book Volume: 18

Pages Range: 765--789

Journal Issue: 4

DOI: 10.1017/S0143385798108337

Abstract

For S-unimodal maps f , we study equilibrium states maximizing the free energies F t () := h() t R log jf 0 jd and the pressure function P (t) := sup F t (). It is shown that if f is uniformly hyperbolic on periodic orbits, then P (t) is analytic for t 1. On the other hand, examples are given where no equilibrium states exist, where equilibrium states are not unique and where the notions of equilibrium state for t = 1 and of observable measure do not coincide.

Authors with CRIS profile

Gerhard Keller Professur für Angewandte Mathematik (Angewandte Analysis)

How to cite

APA:

Bruin, H.P., & Keller, G. (1998). Equilibrium states for S-unimodal maps. Ergodic Theory and Dynamical Systems, 18(4), 765--789. https://dx.doi.org/10.1017/S0143385798108337

MLA:

Bruin, Hendrik Pieter, and Gerhard Keller. "Equilibrium states for S-unimodal maps." Ergodic Theory and Dynamical Systems 18.4 (1998): 765--789.

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