# A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II

Kaloshin V, Hunt BR. 2001. 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. 7(5), 28–36.

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*Journal Article*|

*Published*|

*English*

Author

Kaloshin, Vadim

^{IST Austria}^{}; Hunt, Brian R.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 $n$. 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.

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Publishing Year

Date Published

2001-04-24

Journal Title

Electronic Research Announcements of the American Mathematical Society

Volume

7

Issue

5

Page

28-36

ISSN

IST-REx-ID

### Cite this

Kaloshin V, Hunt BR. 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*. 2001;7(5):28-36. doi:10.1090/s1079-6762-01-00091-9Kaloshin, V., & Hunt, B. R. (2001). 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*. American Mathematical Society. https://doi.org/10.1090/s1079-6762-01-00091-9Kaloshin, Vadim, and Brian R. Hunt. “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*. American Mathematical Society, 2001. https://doi.org/10.1090/s1079-6762-01-00091-9.V. Kaloshin and B. R. Hunt, “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*, vol. 7, no. 5. American Mathematical Society, pp. 28–36, 2001.Kaloshin, Vadim, and Brian R. Hunt. “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*, vol. 7, no. 5, American Mathematical Society, 2001, pp. 28–36, doi:10.1090/s1079-6762-01-00091-9.