@article{b7ff02b3e4a0407e977c337d03b7b777,
title = "Borel subsystems and ergodic universality for compact Zd-systems via specification and beyond",
abstract = "A Borel (Formula presented.) dynamical system (Formula presented.) is {\textquoteleft}almost Borel universal{\textquoteright} 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 {\textquoteleft}generic{\textquoteright} 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.",
keywords = "37A05, 37A35, 37B40, 37B51",
author = "Nishant Chandgotia and Tom Meyerovitch",
note = "Funding Information: We are deeply indebted to Benjy Weiss for many valuable discussions. It was suggested to us by Jerome Buzzi to pursue the almost Borel version of our result. We thank Ron Peled for suggesting the use of reflection positivity and Yinon Spinka for simplifying several arguments regarding graph colorings and graph homomorphisms in Section 9. We thank Dominik Kwietniak for pointing out the recent publications of Guih{\'e}neuf and Lefeuvre. We also thank Jon Aaronson, Tim Austin, Mike Boyle, Raimundo Brice{\~n}o, Mike Hochman, Brian Marcus, Ronnie Pavlov, Brandon Seward, Ay{\c s}e {\c S}ahin, Terry Soo and Spencer Unger for several discussions and encouragement. We thank the Pacific Institute for Mathematical Studies and the Department of Mathematics at the University of British Columbia for warm hospitality. Finally, we thank the anonymous referee for numerous comments and suggestions which improved the presentation significantly and Sebasti{\'a}n Barbieri Lemp for having look at parts of the revised version. Most of the work in this paper was done when the first author was a postdoctoral fellow at Tel Aviv University and the Hebrew University of Jerusalem. Publisher Copyright: {\textcopyright} 2021 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.",
year = "2021",
month = sep,
day = "1",
doi = "10.1112/plms.12398",
language = "English",
volume = "123",
pages = "231--312",
journal = "Proceedings of the London Mathematical Society",
issn = "0024-6115",
publisher = "John Wiley and Sons Ltd",
number = "3",
}