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Mixing completely scrambled system exists | | Jan P. Boroński
; Jiří Kupka
; Piotr Oprocha
; | | Date: |
6 Sep 2016 | | Abstract: | We prove that there exists a topologically mixing homeomorphism which is
completely scrambled. We also prove that for any integer $ngeq 1$ there is a
continuum of topological dimension $n$ supporting a transitive completely
scrambled homeomorphism, and $n$-dimensional compactum supporting a weakly
mixing completely scrambled homeomorphism. This solves a 15 year old open
problem. | | Source: | arXiv, 1609.1631 | | Services: | Forum | Review | PDF | Favorites | |
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