2003/02/15 by Eugene Polulyakh, Polulyakh, Eugene
Computer Science · Mathematics · #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #advanced mathematical theories #math.DS #msc:37B05 #msc:37B20
paper · pdf · doi:10.48550/arxiv.math/0302181
62 pages in LaTeX 2-e
arxiv created 2003/02/15 · arxiv updated 2009/11/30
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 Σ 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).