English

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 n1n\geq 1 there is a continuum of topological dimension nn supporting a transitive completely scrambled homeomorphism, and nn-dimensional compactum supporting a weakly mixing completely scrambled homeomorphism. This solves a 15 year old open problem.

Keywords

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

R2 v1 2026-06-22T15:41:28.189Z