Branched coverings of the sphere having a completely invariant continuum with infinitely many Wada Lakes

TL;DR

This paper constructs a family of smooth degree-2 branched coverings of the sphere with a completely invariant indecomposable continuum and infinitely many Wada Lakes, advancing understanding of complex topological dynamics.

Contribution

It introduces a new family of smooth branched coverings with invariant continua and Wada Lakes, expanding the class of known dynamical systems with such properties.

Findings

Existence of smooth degree-2 branched coverings with invariant continua

Construction of systems with infinitely many Wada Lakes

Contribution to topological dynamics and complex systems

Abstract

We construct a family of smooth branched coverings of degree $2$ of the sphere $S^2$ having a completely invariant indecomposable continuum $K$ and infinitely many Wada Lakes.