## The information topology and true laminations for diffeomorphisms

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- by Meiyu Su PDF
- Conform. Geom. Dyn.
**8**(2004), 36-51 Request permission

## 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.## References

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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
- Received by editor(s): September 10, 2003
- Received by editor(s) in revised form: January 29, 2004
- Published electronically: March 8, 2004
- © Copyright 2004 American Mathematical Society
- 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
- MathSciNet review: 2060377