Extensions of exact and K-mixing dynamical systems
| Autor: | Marco Lenci, Daniele Galli |
|---|---|
| Přispěvatelé: | Galli, Daniele, Lenci, Marco |
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: |
extensions of dynamical systems
exactness K-property decomposition theorem skew products Lorentz gas Lorentz tube Sinai billiard FOS: Mathematics FOS: Physical sciences Statistical and Nonlinear Physics Dynamical Systems (math.DS) Mathematical Physics (math-ph) Mathematics - Dynamical Systems 37A40 37A35 (primary) 37C83 37D25 37A20 (secondary) Mathematical Physics |
| Popis: | We consider extensions of non-singular maps which are exact, respectively K-mixing, or at least have a decomposition into positive-measure exact, respectively K-mixing, components. The fibers of the extension spaces have countable (finite or infinite) cardinality and the action on them is assumed surjective or bijective. We call these systems, respectively, fiber-surjective and fiber-bijective extensions. Technically, they are skew products, though the point of view we take here is not the one generally associated with skew products. Our main results are an Exact and a K-mixing Decomposition Theorem. The latter can be used to show that a large number of periodic Lorentz gases (the term denoting here general group extensions of Sinai billiards, including Lorentz tubes and slabs, in any dimension) are K-mixing. 19 pages, 6 figures. Post-publication. Fixed minor imprecisions in Thms. 2.3 + 2.5, (iv) + (vi) and Prop. 4.1 |
| Databáze: | OpenAIRE |
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