Almost complete Lyapunov spectrum in step skew-products

摘要

We study the spectrum of Lyapunov exponents of a family of partially hyperbolic and topologically transitive local diffeomorphisms that are step skew-products over a horseshoe map, continuing previous investigations. These maps are genuinely non-hyperbolic and the central Lyapunov spectrum contains negative and positive values. We show that, besides one gap, this spectrum is complete. We also investigate how Lyapunov regular points with corresponding (central) exponents are distributed in phase space. The principal ingredients of our proofs are minimality of the underlying iterated function system and shadowing-like arguments.