Communications in Mathematical Physics

, Volume 283, Issue 3, pp 579–611 | Cite as

Equilibrium States for Interval Maps: Potentials with sup φ − inf φ < h top (f)

  • Henk BruinEmail author
  • Mike Todd


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 < h top (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.


Gibbs Measure Induce Scheme Exponential Growth Rate Summable Variation Markov Shift 
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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of SurreySurreyUK
  2. 2.Departamento de Matemática PuraFaculdade de Ciências da Universidade do PortoPortoPortugal

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