Perturbations of flexible Latt\`es maps

TL;DR

This paper demonstrates that flexible Lattès maps can be approximated by rational maps that are strictly postcritically finite but not Lattès maps, expanding understanding of their dynamical properties.

Contribution

It introduces a method to approximate flexible Lattès maps with strictly postcritically finite rational maps that are not Lattès maps, revealing new dynamical approximations.

Findings

Flexible Lattès maps can be approximated by non-Lattès postcritically finite maps.

The approximation preserves key dynamical features while changing the Lattès property.

This advances the understanding of the structure and classification of rational maps.

Abstract

We prove that any Latt\`es map can be approximated by strictly postcritically finite rational maps which are not Latt\`es maps.