Robust Transitivity of Partially Hyperbolic Diffeomorphisms with Interval Central Leaves

2025/09/26 by Li, Wenchao, Shi, Yi, Xia, Mingyang
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.21954

Abstract

For a boundary-preserving partially hyperbolic diffeomorphism with interval central leaves, we completely characterize the C^k-robust transitivity (k≥ 2) by boundary interconnection. As an application, if the boundary SRB measures admit negative central Lyapunov exponents, then boundary interconnection also completely characterizes the phenomenon of robustly intermingled basins for boundary SRB measures.

Citations

• On the number of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms with compact center leaves
• Measures maximizing the entropy for Kan endomorphisms
• A robustly transitive diffeomorphism of Kan's type
• Many intermingled basins in dimension 3
• Geometric and measure-theoretical structures of maps with mostly contracting center

Related

• A robustly transitive diffeomorphism of Kan's type
• Robust transitivity and density of periodic points of partially hyperbolic diffeomorphisms
• Some hyperbolicity revisited and robust transitivity
• Stably ergodic diffeomorphisms which are not partially hyperbolic
• C^k-Robust transitivity for surfaces with boundary