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Topological and measurable dynamics : allostery, quantitative orbit equivalence

Abstract : This PhD thesis lies at the interface between topological dynamics and measurable dynamics. First, I study the notion of allosteric actions. These actions are generically free in the sense of the topology but not generically free in the sense of the measure. This surprising behavior highlights the differences between invariant random subgroups and uniformly recurrent subgroups. The nascent theory of quantitative orbit equivalence is the second topic of this thesis. This is a strengthening of orbit equivalence, which aims to understand how metric structures on the orbits of the actions can be distorted. A large part of my work gravitates around one of the founding result of this theory: Belinskaya's theorem.
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Submitted on : Thursday, June 23, 2022 - 11:49:10 AM
Last modification on : Friday, June 24, 2022 - 3:48:18 AM

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Matthieu Joseph. Topological and measurable dynamics : allostery, quantitative orbit equivalence. Dynamical Systems [math.DS]. Université de Lyon, 2022. English. ⟨NNT : 2022LYSEN021⟩. ⟨tel-03702675⟩

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