On density of positive Lyapunov exponents for C¹ symplectic diffeomorphisms

2015/06/17 by Chao Liang, Liang, Chao
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1506.05181

openalex publication_date 2015/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a 2d-dimensional compact connected Riemannian manifold and ω be a symplectic form on M. In this paper, we prove that a symplectic diffeomorphism, with all Lyapunov exponent zero for almost everywhere, can be C¹ approximated by one with a positive Lyapunov exponent for a positive-measured subset of M. That is, the set \ f∈ Sym¹_ω(M) | · amp;The largest Lyapunov exponent λ₁(f, x) · gt;0
· amp; for a positive measure set \ is dense in Sym¹_ω(M). \endabstract \endcenter

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