Stable manifolds, Horseshoes and Lyapunov exponents for $C^1$ diffeomorphisms without domination
Dynamical Systems
2025-12-02 v1
Abstract
We develop the nonuniformly hyperbolic theory for 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.
Keywords
Cite
@article{arxiv.2512.01269,
title = {Stable manifolds, Horseshoes and Lyapunov exponents for $C^1$ diffeomorphisms without domination},
author = {Yongluo Cao and Zeya Mi and Rui Zou},
journal= {arXiv preprint arXiv:2512.01269},
year = {2025}
}