Entropy of real rational surface automorphisms: Actions on the Fundamental Groups

TL;DR

This paper presents a method to compute and estimate the entropy of real rational surface automorphisms by analyzing their induced actions on the fundamental group, providing new tools for understanding surface dynamics.

Contribution

It introduces a novel approach to compute the induced action on the fundamental group and estimates the entropy growth rate for real rational surface automorphisms.

Findings

Computed induced actions for basic quadratic real automorphisms

Provided a lower bound estimate for entropy based on fundamental group actions

Established a connection between fundamental group growth and surface automorphism entropy

Abstract

This article discusses a method to compute the induced action on the fundamental group of a real rational surface and provides the induced actions for basic quadratic real automorphisms. Using an invariant set in the fundamental group, we introduce a method to estimate a lower bound of the action's growth rate on the fundamental group. The growth rate of this induced action gives a lower bound for the entropy of real surface automorphism.