On the number of periodic points for expansive pseudogroups

We consider weakly expansive holonomy pseudogroup foliations of compact manifolds. Our main results show the number of compact leaves is generally countable, and at most finite for codimension-one cases. We show examples of such foliations, demonstrating the results are sharp. •It describes the peri...

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Bibliographic Details
Published in:Chaos, solitons and fractals solitons and fractals, 2024-09, Vol.186, p.115245, Article 115245
Main Authors: Carrasco, Pablo D., Rego, Elias, Rodriguez Hertz, Jana
Format: Article
Language:English
Subjects:
Epstein filtration
Expansive foliations
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Summary:We consider weakly expansive holonomy pseudogroup foliations of compact manifolds. Our main results show the number of compact leaves is generally countable, and at most finite for codimension-one cases. We show examples of such foliations, demonstrating the results are sharp. •It describes the periodic data in expansive foliation: compact leaves.•Expansive foliations appear naturally in Quantum Gravity and General Relativity.•It introduces new and accessible examples showing that the results are sharp.•It is succinct.
ISSN:0960-0779
DOI:10.1016/j.chaos.2024.115245