The information topology and true laminations for diffeomorphisms
Author:
Meiyu Su
Journal:
Conform. Geom. Dyn. 8 (2004), 3651
MSC (2000):
Primary 37D30; Secondary 37C05
Published electronically:
March 8, 2004
MathSciNet review:
2060377
Fulltext PDF Free Access
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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:
http://dx.doi.org/10.1090/S1088417304001079
PII:
S 10884173(04)001079
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
