On the genericity of positive exponents of conservative skew products with two-dimensional fibers

2018/09/11 by Davi Obata, Mauricio Poletti, Obata, Davi +1
Mathematics · #37D25 #37D30 #37H15 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1809.03874

openalex publication_date 2018/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the existence of positive Lyapunov exponents for three different types of skew products, whose fibers are compact Riemannian surfaces and the action on the fibers are by volume preserving diffeomorphisms. These three types include skew products with a volume preserving Anosov diffeomorphism on the basis; or with a subshift of finite type on the basis preserving a measure with product structure; or locally constant skew products with Bernoulli shifts on the basis. We prove the C¹-density and C^r-openess of the existence of positive Lyapunov exponents on a set of positive measure in the space of such skew products.

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