Linear dynamics induced by odometers
Copyright policy )Linear dynamics induced by odometers
Weighted shifts are an important concrete class of operators in linear dynamics. In particular, they are an essential tool in distinguishing a variety of dynamical properties. Recently, a systematic study of dynamical properties of composition operators on L p L^p spaces has been initiated. This class of operators includes weighted shifts and also allows flexibility in construction of other concrete examples. In this article, we study one such concrete class of operators, namely composition operators induced by measures on odometers. In particular, we study measures on odometers which induce mixing and transitive linear operators on L p L^p spaces.
- University of Campania "Luigi Vanvitelli" Italy
- University of Louisville United States
- University of Palermo Italy
47B33, 37B20 (Primary), 5420 (Secondary), topological transitivity, composition operators, Linear composition operators, Cyclic vectors, hypercyclic and chaotic operators, linear dynamics, Dynamical Systems (math.DS), Topological dynamics, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), topological mixing, odometers, Dynamical aspects of cellular automata, FOS: Mathematics, Notions of recurrence and recurrent behavior in topological dynamical systems, Mathematics - Dynamical Systems
47B33, 37B20 (Primary), 5420 (Secondary), topological transitivity, composition operators, Linear composition operators, Cyclic vectors, hypercyclic and chaotic operators, linear dynamics, Dynamical Systems (math.DS), Topological dynamics, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), topological mixing, odometers, Dynamical aspects of cellular automata, FOS: Mathematics, Notions of recurrence and recurrent behavior in topological dynamical systems, Mathematics - Dynamical Systems
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