Stable manifolds, Horseshoes and Lyapunov exponents for C¹ diffeomorphisms without domination

2025/12/01 by Cao, Yongluo, Mi, Zeya, Zou, Rui
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.01269

Abstract

We develop the nonuniformly hyperbolic theory for C¹ diffeomorphisms admitting continuous invariant splitting without domination. This framework includes stable manifold theorems, shadowing and closing lemmas, the existence of horseshoes and the approximation of Lyapunov exponents. The foundation is a new family of resonance blocks, each arising as the forward limit set of a typical point at carefully chosen resonance times where expansion, contraction and a weak scale-dependent domination coexist.

Citations

• Ledrappier-Young entropy formula for C¹ diffeomorphisms with dominated splitting Part 1: Unstable entropy formula and invariance principle
• C¹ Pesin (un)stable manifold without domination
• Horseshoes and Lyapunov exponents for Banach cocycles over nonuniformly hyperbolic systems
• Nonuniform Hyperbolicity, Global Dominated Splittings and Generic\n Properties of Volume-Preserving Diffeomorphisms

Related

• Nonuniform hyperbolicity for C¹-generic diffeomorphisms
• Nonuniform Hyperbolicity, Global Dominated Splittings and Generic\n Properties of Volume-Preserving Diffeomorphisms
• C¹ Pesin (un)stable manifold without domination
• Non-uniformly hyperbolic endomorphisms
• The approximation of Lyapunov exponents by horseshoes for C¹-diffeomorphisms with dominated splitting