Topological dynamics indexed by words
Copyright policy )Topological dynamics indexed by words
Starting with a combinatorial partition theorem for words over an infinite alphabet dominated by a fixed sequence, established recently by the authors, we prove recurrence results for topological dynamical systems indexed by such words. In this way we extend the classical theory developed by Furstenberg and Weiss of dynamical systems indexed by the natural numbers to systems indexed by words. Moreover, applying this theory to topological systems indexed by semigroups that can be represented as words we get analogous recurrence results for such systems.
20 pages
- National and Kapodistrian University of Athens Greece
- Athens State University United States
Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.), IP-limits, Ramsey theory, General Topology (math.GN), ω-Z⁎-located words, Dynamical Systems (math.DS), 37Bxx (Primary) 54H20 (Secondary), Topological dynamics, rational numbers, \(\omega -\mathbb Z^{*}\)-located words, topological dynamics, Rational numbers, FOS: Mathematics, Geometry and Topology, Mathematics - Dynamical Systems, Mathematics - General Topology
Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.), IP-limits, Ramsey theory, General Topology (math.GN), ω-Z⁎-located words, Dynamical Systems (math.DS), 37Bxx (Primary) 54H20 (Secondary), Topological dynamics, rational numbers, \(\omega -\mathbb Z^{*}\)-located words, topological dynamics, Rational numbers, FOS: Mathematics, Geometry and Topology, Mathematics - Dynamical Systems, Mathematics - General Topology
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