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Conformal Geometry and Dynamics

ISSN 1088-4173

 

 

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
Published electronically: March 8, 2004
MathSciNet review: 2060377
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Abstract: We explore the lamination structure from data supplied by a general measure space $X$ provided with a Borel probability measure $m$. We show that if the data satisfy some typical axioms, then there exists a lamination $\mathcal{L}$ injected in the underlying space $X$whose image fills up the measure $m$. For an arbitrary $C^{1+\alpha}$-diffeomorphism $f$ of a compact Riemannian manifold $M$, we construct the data that naturally possess the properties of the axioms; thus we obtain the stable and unstable laminations $\mathcal{L}^{s/u}$ continuously injected in the stable and unstable partitions $\mathcal{W}^{s/u}$. 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