Approximation of Lyapunov exponents in non-archimedean and complex dynamics

TL;DR

This paper presents methods to approximate Lyapunov exponents for rational functions over various fields, extending beyond the complex numbers to include non-archimedean fields.

Contribution

It introduces two new approaches for approximating Lyapunov exponents in non-archimedean and complex dynamics, broadening the scope of dynamical systems analysis.

Findings

Two approximation methods for Lyapunov exponents are proposed.

The methods apply to rational functions over diverse fields.

Extensions beyond classical complex dynamics are demonstrated.

Abstract

We give two kinds of approximation of Lyapunov exponents of rational functions of degree more than one on the projective line over more general fields than that of complex numbers.