Note on homology of expanding foliations

Radu Saghin

doi:10.3934/dcdss.2009.2.349

Note on homology of expanding foliations

Radu Saghin

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

This note contains some remarks about the homologies that can be associated to a foliation which is invariant and uniformly expanded by a diffeomorphism. We construct a family of 'dynamical' closed currents supported on the foliation which help us relate the geometric volume growth of the leaves under the diffeomorphism with the map induced on homology in the case when these currents have nonzero homology.

Original language	English
Pages (from-to)	349-360
Number of pages	12
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	2
Issue number	2
DOIs	https://doi.org/10.3934/dcdss.2009.2.349
State	Published - Jun 2009
Externally published	Yes

Keywords

Expanding dynamics
Invariant foliations
Ruelle-Sullivan currents

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10.3934/dcdss.2009.2.349

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title = "Note on homology of expanding foliations",

abstract = "This note contains some remarks about the homologies that can be associated to a foliation which is invariant and uniformly expanded by a diffeomorphism. We construct a family of 'dynamical' closed currents supported on the foliation which help us relate the geometric volume growth of the leaves under the diffeomorphism with the map induced on homology in the case when these currents have nonzero homology.",

keywords = "Expanding dynamics, Invariant foliations, Ruelle-Sullivan currents",

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AB - This note contains some remarks about the homologies that can be associated to a foliation which is invariant and uniformly expanded by a diffeomorphism. We construct a family of 'dynamical' closed currents supported on the foliation which help us relate the geometric volume growth of the leaves under the diffeomorphism with the map induced on homology in the case when these currents have nonzero homology.

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KW - Ruelle-Sullivan currents

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Note on homology of expanding foliations

Abstract

Keywords

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