Hausdorff dimension and the dynamics of diffeomorphisms

DOI10.1007/BF02675081zbMath0962.37008OpenAlexW2066062993MaRDI QIDQ1569788

Evgeny V. Shchepin

Publication date: 19 June 2001

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02675081

zbMATH Keywords

Lie groupsHausdorff dimensionHausdorff measureHilbert-Smith conjecturecompact topological group\(p\)-adic transformation groupsdynamics of diffeomorphismsLipschitz actions

Mathematics Subject Classification ID

Compact Lie groups of differentiable transformations (57S15) Orbit growth in dynamical systems (37C35) Dimension theory in general topology (54F45) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Dimension theory of smooth dynamical systems (37C45) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (4)

On the structure of the ring of continuous functions on spaces with \(p\)-adic group of transformations ⋮ The Myers-Steenrod theorem for Finsler manifolds of low regularity ⋮ Diffeomorphism groups of compact manifolds ⋮ On smoothness of compacta

Cites Work

• Unnamed Item
• \(p\)-adic transformation groups
• A proof of the Hilbert-Smith conjecture for actions by Lipschitz maps
• Group actions on manifolds and smooth ambient homogeneity
• On the action of a locally compact group on \(E_n\)
• Locally compact groups of differentiable transformations
• The Hilbert-Smith conjecture for Hölder actions
• $C^1$-homogeneous compacta in $\mathbb {R}^n$ are $C^1$-submanifolds of $\mathbb {R}^n$

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