Complex Perspective for the Projective Heat Map Acting on Pentagons

TL;DR

This paper extends Schwartz's real dynamics of the projective heat map to the complex domain by calculating its first dynamical degree and deriving related dynamical properties.

Contribution

It introduces a complex perspective on the projective heat map and computes its first dynamical degree, providing new insights into its dynamics.

Findings

Computed the first dynamical degree of the complexified heat map

Derived corollaries about the map's complex dynamics

Extended real dynamics results to complex setting

Abstract

We place Schwartz's work on the real dynamics of the projective heat map $H$ into the complex perspective by computing its first dynamical degree and gleaning some corollaries about the dynamics of $H$.