Exponents and Almost Periodic Orbits
Exponents and Almost Periodic Orbits
We introduce the group of exponents of a map of the reals into a metric space and give conditions under which this group embeds in the first Cech cohomology group of the closure of the image of the map. We show that this group generalizes the subgroup of the reals generated by the Fourier-Bohr exponents of an almost periodic orbit and that any minimal almost periodic flow in a complete metric space is determined up to (topological) equivalence by this group. We also develop a way of associating groups with any self-homeomorphism of a metric space that generalizes the rotation number of an orientation-preserving homeomorphism of the circle with irrational rotation number.
To appear in "Toplogy Proceedings"
Rotation numbers and vectors, Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems, Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions, 58F25 (Primary) 43A60 (Secondary), Dynamical Systems (math.DS), Compact groups, almost periodic orbits, rotation number, Dynamics induced by flows and semiflows, FOS: Mathematics, Mathematics - Dynamical Systems
Rotation numbers and vectors, Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems, Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions, 58F25 (Primary) 43A60 (Secondary), Dynamical Systems (math.DS), Compact groups, almost periodic orbits, rotation number, Dynamics induced by flows and semiflows, FOS: Mathematics, Mathematics - Dynamical Systems
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