On projections onto odometers of dynamical systems with the compact phase space

Eugene Polulyakh

Published 2003-02-15Version 1

We investigate projections to odometers (group rotations over adic groups) of topological invertible dynamical systems with discrete time and compact Hausdorff phase space. For a dynamical system $(X, f)$ with a compact phase space we consider the category of its projections onto odometers. We examine the connected partial order relation on the class of all objects of a skeleton of this category. We claim that this partially ordered class always have maximal elements and characterize them. It is claimed also, that this class have a greatest element and is isomorphic to some characteristic for the dynamical system $(X, f)$ subset of the set $\Sigma$ of ultranatural numbers if and only if the dynamical system $(X, f)$ is indecomposable (the space $X$ could not be decomposed into two proper disjoint closed invariant subsets).