Skip to Main Content

Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The information topology and true laminations for diffeomorphisms
HTML articles powered by AMS MathViewer

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
  • Luis Barreira, Yakov Pesin, and Jörg Schmeling, Dimension and product structure of hyperbolic measures, Ann. of Math. (2) 149 (1999), no. 3, 755–783. MR 1709302, DOI 10.2307/121072
  • J.-P. Eckmann and D. Ruelle, Ergodic theory of chaos and strange attractors, Rev. Modern Phys. 57 (1985), no. 3, 617–656. MR 800052, DOI 10.1103/RevModPhys.57.617
  • A. Fathi, M.-R. Herman, and J.-C. Yoccoz, A proof of Pesin’s stable manifold theorem, Geometric dynamics (Rio de Janeiro, 1981) Lecture Notes in Math., vol. 1007, Springer, Berlin, 1983, pp. 177–215. MR 730270, DOI 10.1007/BFb0061417
  • ly F. Ledrappier and L. S. Young, The Metric Entropy of Diffeomorphisms, Part I: Characterization of Measures Satisfying Pesinś Entropy Formula, and Part II: Relations between Entropy, Exponents and Dimension, Annals of Math. (122) (1985), 509–539 and 540–574.
  • Ricardo Mañé, A proof of Pesin’s formula, Ergodic Theory Dynam. Systems 1 (1981), no. 1, 95–102. MR 627789, DOI 10.1017/s0143385700001188
  • os V. I. Oseledec, Multiplicative ergodic theorem, Lyapunov characteristic numbers for dynamical systems, Trans. Mosc. Math. Soc. (19) (198), 197–221. pes1 Ya. B. Pesin, Families of invariant manifolds corresponding to non-zero characteristic exponents, English Transl., Math USSR-Izv. (10) (1976), 1261–1305. pes2 —, Characteristic Lyapunov exponents and smooth ergodic theory, English transl., Russian Math. Surveys (32) (1977), 55–114.
  • Charles Pugh and Michael Shub, Ergodic attractors, Trans. Amer. Math. Soc. 312 (1989), no. 1, 1–54. MR 983869, DOI 10.1090/S0002-9947-1989-0983869-1
  • G. E. Shilov and B. L. Gurevich, Integral, measure and derivative: a unified approach, Revised English edition, Dover Books on Advanced Mathematics, Dover Publications, Inc., New York, 1977. Translated from the Russian and edited by Richard A. Silverman. MR 0466463
  • Meiyu Su, Measured solenoidal Riemann surfaces and holomorphic dynamics, J. Differential Geom. 47 (1997), no. 1, 170–195. MR 1601438
  • su2 —, Laminations for hyperbolic measures, Preprint, May 2003. ss M. Su and D. Sullivan, Laminations for endmorphisms, in preparation, 2003.
  • Dennis Sullivan, Bounds, quadratic differentials, and renormalization conjectures, American Mathematical Society centennial publications, Vol. II (Providence, RI, 1988) Amer. Math. Soc., Providence, RI, 1992, pp. 417–466. MR 1184622
  • Dennis Sullivan, Linking the universalities of Milnor-Thurston, Feigenbaum and Ahlfors-Bers, Topological methods in modern mathematics (Stony Brook, NY, 1991) Publish or Perish, Houston, TX, 1993, pp. 543–564. MR 1215976
Similar Articles
  • Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2000): 37D30, 37C05
  • Retrieve articles in all journals with MSC (2000): 37D30, 37C05
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