Quas, A;
Soo, T;
(2016)
Ergodic universality of some topological dynamical systems.
Transactions of the American Mathematical Society
, 368
(6)
pp. 4137-4170.
10.1090/tran/6489.
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Abstract
The Krieger generator theorem says that every invertible ergodic measure-preserving system with finite measure-theoretic entropy can be embedded into a full shift with strictly greater topological entropy. We extend Krieger's theorem to include toral automorphisms and, more generally, any topological dynamical system on a compact metric space that satisfies almost weak specification, asymptotic entropy expansiveness, and the small boundary property. As a corollary, one obtains a complete solution to a natural generalization of an open problem in Halmos's 1956 book regarding an isomorphism invariant that he proposed.
| Type: | Article |
|---|---|
| Title: | Ergodic universality of some topological dynamical systems |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1090/tran/6489 |
| Publisher version: | https://doi.org/10.1090/tran/6489 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10089079 |
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