Slow Entropy of Some Parabolic Flows

Adam Kanigowski, Kurt Vinhage, Daren Wei

Research output: Contribution to journalArticle

Abstract

We study nontrivial entropy invariants in the class of parabolic flows on homogeneous spaces, quasi-unipotent flows. We show that topological complexity (i.e., slow entropy) can be computed directly from the Jordan block structure of the adjoint representation. Moreover using uniform polynomial shearing we are able to show that the metric orbit growth (i.e., slow entropy) coincides with the topological one for quasi-unipotent flows (this also applies to the non-compact case). Our results also apply to sequence entropy. We establish criterion for a system to have trivial topological complexity and give some examples in which the measure-theoretic and topological complexities do not coincide for uniquely ergodic systems, violating the intuition of the classical variational principle.

Original languageEnglish (US)
Pages (from-to)449-474
Number of pages26
JournalCommunications In Mathematical Physics
Volume370
Issue number2
DOIs
Publication statusPublished - Sep 1 2019

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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