PulseExploreJournal ClubDebatesTrendingResearchersJournals
Instagram
HomeExploreJournal ClubTrending
Synapse
⌘+K
Synapse
May 27, 20260 citationsOpen Access

On the dynamics of composition operators: supercyclicity, odometers and translations

FBFrédéric BayartÉMÉtienne Matheron

Key Points

  • This research aims to explore the dynamical properties of composition operators on Banach spaces, focusing on their supercyclicity and hypercyclicity.
  • Studied composition operators induced by odometers to create new examples and counter-examples.
  • Analyzed general statements about the behavior of these operators on Lp-spaces.
  • Identified new examples and counter-examples related to the dynamics of composition operators induced by odometers.
  • Provided general insights on supercyclicity and frequent hypercyclicity of composition operators in Lp-spaces.

Abstract

We study the dynamical properties of composition operators acting on Banach spaces of measurable functions. In particular, we study in some detail the composition operators induced by odometers, which allows us to give a variety of new examples and counter-examples. We also get general statements about supercyclicity and frequent hypercyclicity of composition operators on L\ₚ-spaces.

Ask AI
Helpful
Bookmark
Share
View Full Paper

Cite This Study

Bayart et al. (2026) studied this question.

synapsesocial.com/papers/6a168b040c924ddd1bd59d50https://doi.org/10.48550/arxiv.2605.23736
Ask AI
Helpful
Bookmark
Share
View Full Paper