Borel subsystems and ergodic universality for compact Zd-systems via specification and beyond

Nishant Chandgotia, Tom Meyerovitch

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

A Borel (Formula presented.) dynamical system (Formula presented.) is ‘almost Borel universal’ if any free Borel (Formula presented.) dynamical system (Formula presented.) of strictly lower entropy is isomorphic to a Borel subsystem of (Formula presented.), after removing a null set. We obtain and exploit a new sufficient condition for a topological (Formula presented.) dynamical system to be almost Borel universal. We use our main result to deduce various conclusions and answer a number of questions. Along with additional results, we prove that a ‘generic’ homeomorphism of a compact manifold of topological dimension at least two can model any ergodic transformation, that non-uniform specification implies almost Borel universality, and that 3-colorings in (Formula presented.) and dimers in (Formula presented.) are almost Borel universal.

Original languageEnglish
Pages (from-to)231-312
Number of pages82
JournalProceedings of the London Mathematical Society
Volume123
Issue number3
DOIs
StatePublished - 1 Sep 2021

Keywords

  • 37A05
  • 37A35
  • 37B40
  • 37B51

ASJC Scopus subject areas

  • General Mathematics

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