2009/07/14 by Godofredo Iommi, Mike Todd · 1 citation
Mathematics · #Absolute continuity #Class (philosophy) #Convexity #Formalism (music) #Invariant (physics) #Lebesgue integration #Lebesgue measure #Mathematical Dynamics and Fractals #Nonlinear Partial Differential Equations #Stochastic processes and statistical mechanics #Uniqueness #math.DS
paper · pdf · doi:10.1007/s00220-010-1112-x
published as Communications in Mathematical Physics 300, 65-94 (2010)
arxiv created 2009/07/14 · openalex publication_date 2010/08/20 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.