Mixing completely scrambled system exists
Dynamical Systems
2017-01-30 v2
Abstract
We prove that there exists a topologically mixing homeomorphism which is completely scrambled. We also prove that for any integer there is a continuum of topological dimension supporting a transitive completely scrambled homeomorphism, and -dimensional compactum supporting a weakly mixing completely scrambled homeomorphism. This solves a 15 year old open problem.
Cite
@article{arxiv.1609.01631,
title = {Mixing completely scrambled system exists},
author = {Jan P. Boroński and Jiří Kupka and Piotr Oprocha},
journal= {arXiv preprint arXiv:1609.01631},
year = {2017}
}
Comments
To appear in Ergodic Theory and Dynamical Systems