Analytic skew products of quadratic polynomials over circle expanding maps

TL;DR

This paper proves that certain dynamical systems called Viana maps, with specific coupling functions, exhibit two positive Lyapunov exponents almost everywhere, indicating complex chaotic behavior.

Contribution

It establishes the existence of two positive Lyapunov exponents for Viana maps with non-constant real analytic couplings, extending understanding of their chaotic dynamics.

Findings

Viana maps have two positive Lyapunov exponents almost everywhere.

The result applies to Viana maps with arbitrarily non-constant real analytic coupling functions.

The work advances the understanding of chaos in skew product systems.

Abstract

We prove that a Viana map with an arbitrarily non-constant real analytic coupling function admits two positive Lyapunov exponents almost everywhere.