Polynomial entropy of induced maps of circle and interval homeomorphisms

TL;DR

This paper calculates the polynomial entropy of induced maps on hyperspaces for homeomorphisms of intervals and circles with finitely many non-wandering points, providing insights into their dynamical complexity.

Contribution

It introduces a method to compute polynomial entropy for induced hyperspace maps of circle and interval homeomorphisms with finitely many non-wandering points.

Findings

Polynomial entropy is explicitly computed for these induced maps.

Results reveal the relationship between non-wandering points and entropy values.

The work advances understanding of dynamical complexity in low-dimensional systems.

Abstract

We compute the polynomial entropy of the induced maps on hyperspace for a homeomorphism $f$ of an interval or a circle with finitely many non-wandering points.