A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II
Authors:
Vadim Yu. Kaloshin and Brian R. Hunt
Journal:
Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 2836
MSC (2000):
Primary 37C20, 37C27, 37C35, 34C25, 34C27
Published electronically:
April 24, 2001
MathSciNet review:
1826993
Fulltext PDF Free Access
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Abstract: We continue the previous article's discussion of bounds, for prevalent diffeomorphisms of smooth compact manifolds, on the growth of the number of periodic points and the decay of their hyperbolicity as a function of their period . In that article we reduced the main results to a problem, for certain families of diffeomorphisms, of bounding the measure of parameter values for which the diffeomorphism has (for a given period ) an almost periodic point that is almost nonhyperbolic. We also formulated our results for dimensional endomorphisms on a compact interval. In this article we describe some of the main techniques involved and outline the rest of the proof. To simplify notation, we concentrate primarily on the dimensional case.
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Additional Information
Vadim Yu. Kaloshin
Affiliation:
Fine Hall, Princeton University, Princeton, NJ 08544
Email:
kaloshin@math.princeton.edu
Brian R. Hunt
Affiliation:
Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742
Email:
bhunt@ipst.umd.edu
DOI:
http://dx.doi.org/10.1090/S1079676201000919
PII:
S 10796762(01)000919
Keywords:
Periodic points,
prevalence,
diffeomorphisms
Received by editor(s):
December 21, 2000
Published electronically:
April 24, 2001
Communicated by:
Svetlana Katok
Article copyright:
© Copyright 2001
American Mathematical Society
