Transitivity and an abelian Livsic theorem for covers

2025/12/03 by Mark Pollicott, Pollicott, Mark, Richard Sharp +1
Mathematics · Physics and Astronomy · #37C05 #37C10 #37D20 #37D40 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2512.03699

openalex publication_date 2025/12/03 · openalex created_date 2025/12/05 · openalex updated_date 2026/07/28

Abstract

We show that the abelian Livšic theorem recently obtained by A. Gogolev and F. Rodriguez Hertz for null-homologous periodic orbits of homologically full Anosov flows continues to hold when restricted to periodic orbits which are trivial with respect to any regular cover for which the lifted flow is transitive.

Citations

• Transitive Anosov flows on non-compact manifolds
• Abelian Livsic theorems for Anosov flows
• Marked length spectrum rigidity from rigidity on subsets
• Marked length pattern rigidity for arithmetic manifolds
• Abelian Livshits theorems and geometric applications
• The marked length spectrum of Anosov manifolds
• Livšic Theorems for Non-Commutative Groups including Diffeomorphism Groups and Results on the Existence of Conformal Structures for Anosov Systems

Related

• Abelian Livsic theorems for Anosov flows
• Abelian Livshits theorems and geometric applications
• Transitivity of Surface Dynamics Lifted to Abelian Covers
• Livšic Theorems for Non-Commutative Groups including Diffeomorphism Groups and Results on the Existence of Conformal Structures for Anosov Systems
• Transitive Anosov flows on non-compact manifolds