Geometric properties of partially hyperbolic measures and applications to measure rigidity

2023/02/25 by Alex Eskin, Eskin, Alex, Rafaël Potrie +3 · 1 citation
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2302.12981

openalex publication_date 2023/02/25 · openalex created_date 2023/03/03 · openalex updated_date 2026/07/28

Abstract

We give a geometric characterization of the quantitative non-integrability, introduced by Katz, of strong stable and unstable bundles of partially hyperbolic measures and sets in dimension 3. This is done via the use of higher order templates for the invariant bundles. Using the recent work of Katz, we derive some consequences, including the measure rigidity of uu-states and the existence of physical measures.

Cited by

• Measure Rigidity beyond Homogeneous Dynamics
• Rigidity of U-Gibbs measures near conservative Anosov diffeomorphisms on \mathbbT³

Related

• Integrable measure equivalence and rigidity of hyperbolic lattices
• Rigidity, lattices and invariant measures beyond homogeneous dynamics
• U-Gibbs measure rigidity for partially hyperbolic endomorphisms on surfaces
• Local Rigidity of Higher Rank Homogeneous Abelian Actions: a Complete Solution via the Geometric Method
• Measure rigidity for generalized u-Gibbs states and stationary measures via the factorization method