The information topology and true laminations for diffeomorphisms

Author:
Meiyu Su

Journal:
Conform. Geom. Dyn. **8** (2004), 36-51

MSC (2000):
Primary 37D30; Secondary 37C05

DOI:
https://doi.org/10.1090/S1088-4173-04-00107-9

Published electronically:
March 8, 2004

MathSciNet review:
2060377

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Abstract | References | Similar Articles | Additional Information

Abstract: We explore the lamination structure from data supplied by a general measure space provided with a Borel probability measure . We show that if the data satisfy some typical axioms, then there exists a lamination injected in the underlying space whose image fills up the measure . For an arbitrary -diffeomorphism of a compact Riemannian manifold , we construct the data that naturally possess the properties of the axioms; thus we obtain the stable and unstable laminations continuously injected in the stable and unstable partitions . These laminations intersect at almost every regular point for the measure.

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Additional Information

**Meiyu Su**

Affiliation:
Mathematics Department, Long Island University, Brooklyn Campus, 1 University Plaza, Brooklyn, New York 11201

Email:
msu@liu.edu

DOI:
https://doi.org/10.1090/S1088-4173-04-00107-9

Keywords:
$C^{1 +\alpha}$-diffeomorphisms on Riemannian manifolds,
stable and unstable manifolds and partitions,
laminations,
Pesin boxes,
and information topology

Received by editor(s):
September 10, 2003

Received by editor(s) in revised form:
January 29, 2004

Published electronically:
March 8, 2004

Article copyright:
© Copyright 2004
American Mathematical Society