6533b85afe1ef96bd12b97fd

RESEARCH PRODUCT

Linear dynamics induced by odometers

Emma D'anielloDonatella BongiornoL. Di PiazzaUdayan B. Darji

subject

Linear dynamics composition operators topological mixing topological transitivity odometers47B33 37B20 (Primary) 5420 (Secondary)Settore MAT/05 - Analisi MatematicaApplied MathematicsGeneral MathematicsDynamics (mechanics)FOS: MathematicsDynamical Systems (math.DS)Statistical physicsMathematics - Dynamical SystemsOdometerMathematics

description

Weighted shifts are an important concrete class of operators in linear dynamics. In particular, they are an essential tool in distinguishing variety dynamical properties. Recently, a systematic study of dynamical properties of composition operators on $L^p$ 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 $L^p$ spaces.

yearjournalcountryeditionlanguage
2022-03-28Proceedings of the American Mathematical Society
https://doi.org/10.1090/proc/15354