Communications in Mathematical Physics

, Volume 300, Issue 1, pp 65–94

Natural Equilibrium States for Multimodal Maps

Authors

    • Facultad de MatemáticasPontificia Universidad Católica de Chile (PUC)
  • Mike Todd
    • Departamento de Matemática PuraFaculdade de Ciências da Universidade do Porto
    • Department of Mathematics and StatisticsBoston University
Article

DOI: 10.1007/s00220-010-1112-x

Cite this article as:
Iommi, G. & Todd, M. Commun. Math. Phys. (2010) 300: 65. doi:10.1007/s00220-010-1112-x

Abstract

This paper is devoted to the study of the thermodynamic formalism for a class of real multimodal maps. This class contains, but it is larger than, Collet-Eckmann. For a map in this class, we prove existence and uniqueness of equilibrium states for the geometric potentials −t log |Df|, for the largest possible interval of parameters t. We also study the regularity and convexity properties of the pressure function, completely characterising the first order phase transitions. Results concerning the existence of absolutely continuous invariant measures with respect to the Lebesgue measure are also obtained.

Copyright information

© Springer-Verlag 2010