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arXiv · 2512.01269

Stable manifolds, Horseshoes and Lyapunov exponents for $C^1$ diffeomorphisms without domination

Yongluo Cao·Zeya Mi·Rui Zou
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Abstract

We develop the nonuniformly hyperbolic theory for $C^1$ 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.

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Yongluo Cao, Zeya Mi, Rui Zou. 2025-12-01. Stable manifolds, Horseshoes and Lyapunov exponents for $C^1$ diffeomorphisms without domination. https://arxiv.org/abs/2512.01269

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