Equilibrium States for Interval Maps: Potentials with sup φ − inf φ < htop(f)
By Henk Bruin, Mike Todd. 2007
65 citations recorded by the source corpus.
We study an inducing scheme approach for smooth interval maps to prove existence and uniqueness of equilibrium states for potentials φ with the ‘bounded range’ condition sup φ − inf φ < htop(f), first used by Hofbauer and Keller [HK]. We compare our results to Hofbauer and Keller’s use of Perron-Frobenius operators. We demonstrate that this ‘bounded range’ condition on the potential is important even if the potential is Hölder continuous. We also prove analyticity of the pressure in this context.
Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/87913d76ba54363d2c0a38748c221af9def86c5d
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In Applied Mathematics
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Expanding Measures (2008, background): “Future applications Recently there was an increasing development of the study of the thermodynamic formalism beyond the uniformly hyperbolic context (including countable Markov shift) by several authors (this list is certainly not complete): Araujo [7], Arbieto, Matheus, Oliveira, Varandas, Viana [8”
- Equilibrium measures for maps with inducing schemes (2006, background): “By [ BK98 , Proposition 3.1], any invariant measure has uniformly positive Lyapunov exponent.”
- Nice Inducing Schemes and the Thermodynamics of Rational Maps (2008, result): “In the case of a general transitive multimodal map, a result analogous to Theorem A was shown by Bruin and Todd in [BT08, Theorem 6] for t in a neighborhood of 0. Similar results for t in a neighborhood of [0,1] were shown by Pesin and Senti in [PS08] for multimodal maps satisfying the Collet-Eckman”