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Israel Journal of Mathematics

, Volume 225, Issue 2, pp 609–659 | Cite as

Entropy in the cusp and phase transitions for geodesic flows

  • Godofredo Iommi
  • Felipe Riquelme
  • Anibal Velozo
Article
  • 33 Downloads

Abstract

In this paper we study the geodesic flow for a particular class of Riemannian non-compact manifolds with variable pinched negative sectional curvature. For a sequence of invariant measures we are able to prove results relating the loss of mass and bounds on the measure entropies. We compute the entropy contribution of the cusps. We develop and study the corresponding thermodynamic formalism. We obtain certain regularity results for the pressure of a class of potentials. We prove that the pressure is real analytic until it undergoes a phase transition, after which it becomes constant. Our techniques are based on the one hand on symbolic methods and Markov partitions, and on the other on geometric techniques and approximation properties at the level of groups.

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Copyright information

© Hebrew University of Jerusalem 2018

Authors and Affiliations

  • Godofredo Iommi
    • 1
  • Felipe Riquelme
    • 2
  • Anibal Velozo
    • 3
  1. 1.Facultad de MatemáticasPontificia Universidad Católica de Chile (PUC)SantiagoChile
  2. 2.Instituto de MatemáticasPontificia Universidad Católica de ValparaísoCerro Barón, ValparaísoChile
  3. 3.Princeton UniversityPrincetonUSA

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