Non-reversibility and self-joinings of higher orders for ergodic flows

Frączek, Krzysztof; Kułaga, Joanna; Lemańczyk, Mariusz

doi:10.48550/arxiv.1206.3053

Cited by 1 publication

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“…Clearly, in the setting of dynamical systems, one could equally well consider the analogous questions for the measure-theoretic centraliser and normaliser, and this is indeed frequently done in the literature; compare [39,70,35] and references therein. Since, in many relevant cases, the measure-theoretic symmetry groups turn out to be topological (see [70] for results in this direction), we concentrate on the latter situation in this overview.…”

Section: General Setting and Notionsmentioning

confidence: 99%

A Brief Guide to Reversing and Extended Symmetries of Dynamical Systems

Baake

2018

Lecture Notes in Mathematics

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The reversing symmetry group is a well-studied extension of the symmetry group of a dynamical system, the latter being defined by the action of a single homeomorphism on a topological space. While it is traditionally considered in nonlinear dynamics, where the space is simple but the map is complicated, it has an interesting counterpart in symbolic dynamics, where the map is simple but the space is not. Moreover, there is an interesting extension to the case of higher-dimensional shifts, where a similar concept can be introduced via the centraliser and the normaliser of the acting group in the full automorphism group of the shift space. We recall the basic notions and review some of the known results, in a fairly informal manner, to give a first impression of the phenomena that can show up in the extension from the centraliser to the normaliser, with some emphasis on recent developments.

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Section: General Setting and Notionsmentioning

confidence: 99%

A Brief Guide to Reversing and Extended Symmetries of Dynamical Systems

Baake

2018

Lecture Notes in Mathematics

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Non-reversibility and self-joinings of higher orders for ergodic flows

Cited by 1 publication

References 10 publications

A Brief Guide to Reversing and Extended Symmetries of Dynamical Systems

A Brief Guide to Reversing and Extended Symmetries of Dynamical Systems

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