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Measure-theoretic sequence entropy pairs and mean sensitivity

Part of: Ergodic theory Topological dynamics

Published online by Cambridge University Press:  19 September 2023

FELIPE GARCÍA-RAMOS Open the ORCID record for FELIPE GARCÍA-RAMOS [Opens in a new window]  and
VÍCTOR MUÑOZ-LÓPEZ
FELIPE GARCÍA-RAMOS*
Affiliation:
Universidad Autonoma de San Luis Potosi, San Luis Potosi 78000, Mexico (e-mail: soygenn@gmail.com) Faculty of Mathematics and Computer Science, Jagiellonian University, Profesora Stanisława Łojasiewicza 6, 30-348 Kraków, Poland
VÍCTOR MUÑOZ-LÓPEZ
Affiliation:
Universidad Autonoma de San Luis Potosi, San Luis Potosi 78000, Mexico (e-mail: soygenn@gmail.com)
*
e-mail: fgramos@conahcyt.mx
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Abstract

We characterize measure-theoretic sequence entropy pairs of continuous actions of abelian groups using mean sensitivity. This addresses an open question of Li and Yu [On mean sensitive tuples. J. Differential Equations 297 (2021), 175–200]. As a consequence of our results, we provide a simpler characterization of Kerr and Li’s independence sequence entropy pairs ($\mu $-IN-pairs) when the measure is ergodic and the group is abelian.

Keywords

sequence entropy pairsmean sensitivityentropy pairsIN-pairs

MSC classification

Primary: 37A15: General groups of measure-preserving transformations 37A35: Entropy and other invariants, isomorphism, classification 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 44 , Issue 6 , June 2024 , pp. 1531 - 1540
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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