Every nondegenerate Peano continuum admits a pure mixing selfmap

TL;DR

The paper proves that all Peano continua can have a topologically mixing selfmap with dense periodic points, expanding understanding of dynamical systems on such spaces.

Contribution

It introduces a construction of mixing maps on Peano continua that are not exact, with dense periodic points, a novel dynamical property for these spaces.

Findings

Every Peano continuum admits a topologically mixing map.

Constructed maps have a dense set of periodic points.

Maps are not exact, showing new dynamical possibilities.

Abstract

We prove that every Peano continuum (a space that is a continuous image of $[0,1]$) admits a topologically mixing but not exact map. The constructed map has a dense set of periodic points.