Geodesic
A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II
Kaloshin, Vadim1 ; Hunt, Brian2
1 Fine Hall, Princeton University, Princeton, NJ 08544
2 Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742
Electronic research announcements of the American Mathematical Society, Tome 07 (2001), pp. 28-36 Cet article a éte moissonné depuis la source American Mathematical Society

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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 $n$. 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 $n$) an almost periodic point that is almost nonhyperbolic. We also formulated our results for $1$-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 $1$-dimensional case.
DOI : 10.1090/S1079-6762-01-00091-9

Kaloshin, Vadim 1 ; Hunt, Brian 2

1 Fine Hall, Princeton University, Princeton, NJ 08544
2 Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742 
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Kaloshin, Vadim; Hunt, Brian. A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II. Electronic research announcements of the American Mathematical Society, Tome 07 (2001), pp. 28-36. doi: 10.1090/S1079-6762-01-00091-9

[1] Golubitsky, M., Guillemin, V. Stable mappings and their singularities 1973

[2] Grigoriev, A., Yakovenko, S. Topology of generic multijet preimages and blow-up via Newton interpolation J. Differential Equations 1998 349 362

[3] Santaló, Luis A. Integral geometry and geometric probability 1976

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