John Banks

Regular periodic decompositions for topologically transitive maps

One may often decompose the domain of a topologically transitive map into finitely many regular closed pieces with nowhere dense overlap in such a way that these pieces map into one another in a periodic fashion. We call decompositions of this kind regular periodic decompositions and refer to the number of pieces as the length of the decomposition. If

Weak mixing implies mixing for maps on topological graphs

f

Smale's Horseshoe map via ternary numbers

is topologically transitive but

Chaos for induced hyperspace maps

f^{n}

Chaos: A Mathematical Introduction

is not, then

Topological mapping properties defined by digraphs

f

Dynamics of spacing shifts

has a regular periodic decomposition of some length dividing

A note on equivalent definitions of topological transitivity

n

Transitive sofic spacing shifts

. Although a decomposition of a given length is unique, a map may have many decompositions of different lengths. The set of lengths of decompositions of a given map is an ideal in the lattice of natural numbers ordered by divisibility, which we call the decomposition ideal of

Chaos: Mappings and orbits

f