The Lyapunov spectrum as the Newton method

TL;DR

This paper establishes a novel connection between the Lyapunov spectrum of cookie-cutter maps and the Newton-Raphson method applied to the pressure function's derivative, providing a new computational perspective.

Contribution

It demonstrates that for cookie-cutter maps, the Lyapunov spectrum can be obtained via the Newton method on the pressure function's derivative, linking dynamical systems and numerical analysis.

Findings

Lyapunov spectrum equals Newton-Raphson map for pressure derivative

Provides a new computational approach for Lyapunov spectra

Bridges dynamical systems theory with numerical methods

Abstract

For a class of dynamical systems, the cookie-cutter maps, we prove that the Lyapunov spectrum coincides with the map given by the Newton-Raphson method applied to the derivative of the pressure function.