On mostly expanding diffeomorphisms

2015/12/03 by Andersson, Martin, Vásquez, Carlos H. · 3 citations
#37A25 #37CD30 #37D25 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1512.01046

Abstract

In this work we study the class of mostly expanding partially hyperbolic diffeomorphisms. We prove that such class is C^r-open, r>1, among the partially hyperbolic diffeomorphisms (in the narrow sense) and we prove that the mostly expanding condition guarantee the existence of physical measures and provide more information about the statistics of the system. Mañé's classical derived-from-Anosov diffeomorphism on \mathbbT³ belongs to this set.

Cited by

• Variety of physical measures in partially hyperbolic systems with multi 1-D centers
• Technical Developments of DA on \mathbbT³
• Stochastic stability of physical measures in conservative systems

Related

• Geometrical and measure-theoretic structures of maps with mostly expanding center
• SRB measures for mostly expanding partially hyperbolic diffeomorphisms via the variational approach
• Statistical stability of mostly expanding diffeomorphisms
• Entropy along expanding foliations
• Entropy properties of mostly expanding partially hyperbolic diffeomorphisms