The C¹ density of nonuniform hyperbolicity in C ^r conservative diffeomorphisms

2015/08/27 by Liang, Chao, Yang, Yun
#37C25 #37D25 #37D30 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1508.06714

Abstract

Let \Diff ^r_m(M) be the set of C ^r volume-preserving diffeomorphisms on a compact Riemannian manifold M (dim M≥ 2). In this paper, we prove that the diffeomorphisms without zero Lyapunov exponents on a set of positive volume are C¹ dense in \Diff ^r_m(M), r≥ 1. We also prove a weaker result for symplectic diffeomorphisms Sym^r_ω(M), r≥1 saying that the symplectic diffeomorphisms with non-zero Lyapunov exponents on a set of positive volume are C¹ dense in Sym^r_ω(M), r≥1 .

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