Birkhoff and Lyapunov spectra on planar self-affine sets

TL;DR

This paper computes the Birkhoff and Lyapunov spectra for a class of planar self-affine sets under specific irreducibility and open set conditions, advancing understanding of their dynamical and geometric properties.

Contribution

It provides explicit calculations of the Birkhoff and Lyapunov spectra for strongly irreducible planar self-affine sets satisfying the strong open set condition, a novel contribution in this area.

Findings

Calculated the Birkhoff spectrum for continuous potentials.

Determined the Lyapunov spectrum for the given sets.

Extended the understanding of dynamical spectra in self-affine fractals.

Abstract

Working on strongly irreducible planar self-affine sets satisfying the strong open set condition, we calculate the Birkhoff spectrum of continuous potentials and the Lyapunov spectrum.