On notions of determinism in topological dynamics

Michael Hochman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We examine the relations between topological entropy, invertibility, and prediction in topological dynamics. We show that topological determinism in the sense of Kamińsky, Siemaszko, and Szymański imposes no restriction on invariant measures except zero entropy. Also, we develop a new method for relating topological determinism and zero entropy, and apply it to obtain a multidimensional analog of this theory. We examine prediction in symbolic dynamics and show that while the condition that each past admits a unique future only occurs in finite systems, the condition that each past has a bounded number of futures imposes no restriction on invariant measures except zero entropy. Finally, we give a negative answer to a question of Eli Glasner by constructing a zero-entropy system with a globally supported ergodic measure in which every point has multiple preimages.

Original languageAmerican English
Pages (from-to)119-140
Number of pages22
JournalErgodic Theory and Dynamical Systems
Volume32
Issue number1
DOIs
StatePublished - Feb 2012
Externally publishedYes

Fingerprint

Dive into the research topics of 'On notions of determinism in topological dynamics'. Together they form a unique fingerprint.

Cite this