Mostly nonuniformly sectional expanding systems

2025/08/08 by Araújo, Vitor, Salgado, Luciana
#37C10 #37D25 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.06233

Abstract

We introduce the notion of mostly nonuniform sectional expanding (MNUSE) for singular flows which encompasses the notions of sectional hyperbolicity, asymptotically sectional and multisingular hyperbolicity. We exhibit an example of a C¹ nonuniformly sectional hyperbolic set satisfying MNUSE, which is neither sectional hyperbolic nor asymptotically sectional hyperbolic. Moreover, under some smoothness assumptions together with, either the dimension or the sign of Lyapunov exponents along the central subbundle, we show that attracting MNUSE sets support a physical/SRB measure. This measure is unique if the dynamics is transitive.

Citations

• C¹ Pesin (un)stable manifold without domination
• Mixing rates of the geometrical neutral Lorenz model
• Contributions to the Theory of Asymptotically Sectional Hyperbolic Flows
• On Chaotic Behavior of ASH Attractors
• Physical measures for mostly sectional expanding flows
• Star fows and multisingular hyperbolicity
• On a differentiable linearization theorem of Philip Hartman
• New Criteria of Generic Hyperbolicity based on Periodic Points
• Stably ergodic diffeomorphisms which are not partially hyperbolic

Related

• Physical measures for asymptotically sectional expanding flows in higher co-dimensions
• Physical measures for mostly sectional expanding flows
• Contributions to the Theory of Asymptotically Sectional Hyperbolic Flows
• Symbolic dynamics for nonuniformly hyperbolic maps with singularities in high dimension
• SRB measures for partially hyperbolic flows with mostly expanding center