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