---
_id: '8521'
abstract:
- lang: eng
  text: 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.
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
  full_name: Kaloshin, Vadim
  id: FE553552-CDE8-11E9-B324-C0EBE5697425
  last_name: Kaloshin
  orcid: 0000-0002-6051-2628
- first_name: Brian R.
  full_name: Hunt, Brian R.
  last_name: Hunt
citation:
  ama: Kaloshin V, Hunt BR. A stretched exponential bound on the rate of growth of
    the number of periodic points for prevalent diffeomorphisms II. <i>Electronic
    Research Announcements of the American Mathematical Society</i>. 2001;7(5):28-36.
    doi:<a href="https://doi.org/10.1090/s1079-6762-01-00091-9">10.1090/s1079-6762-01-00091-9</a>
  apa: Kaloshin, V., &#38; Hunt, B. R. (2001). A stretched exponential bound on the
    rate of growth of the number of periodic points for prevalent diffeomorphisms
    II. <i>Electronic Research Announcements of the American Mathematical Society</i>.
    American Mathematical Society. <a href="https://doi.org/10.1090/s1079-6762-01-00091-9">https://doi.org/10.1090/s1079-6762-01-00091-9</a>
  chicago: 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.” <i>Electronic Research Announcements of the American Mathematical Society</i>.
    American Mathematical Society, 2001. <a href="https://doi.org/10.1090/s1079-6762-01-00091-9">https://doi.org/10.1090/s1079-6762-01-00091-9</a>.
  ieee: 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,” <i>Electronic
    Research Announcements of the American Mathematical Society</i>, vol. 7, no. 5.
    American Mathematical Society, pp. 28–36, 2001.
  ista: 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.
  mla: 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.”
    <i>Electronic Research Announcements of the American Mathematical Society</i>,
    vol. 7, no. 5, American Mathematical Society, 2001, pp. 28–36, doi:<a href="https://doi.org/10.1090/s1079-6762-01-00091-9">10.1090/s1079-6762-01-00091-9</a>.
  short: V. Kaloshin, B.R. Hunt, Electronic Research Announcements of the American
    Mathematical Society 7 (2001) 28–36.
date_created: 2020-09-18T10:49:43Z
date_published: 2001-04-24T00:00:00Z
date_updated: 2021-01-12T08:19:51Z
day: '24'
doi: 10.1090/s1079-6762-01-00091-9
extern: '1'
fulldoi: https://doi.org/10.1090/s1079-6762-01-00091-9
intvolume: '         7'
issue: '5'
keyword:
- General Mathematics
language:
- iso: eng
month: '04'
oa_version: None
page: 28-36
publication: Electronic Research Announcements of the American Mathematical Society
publication_identifier:
  issn:
  - 1079-6762
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
status: public
title: A stretched exponential bound on the rate of growth of the number of periodic
  points for prevalent diffeomorphisms II
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7
year: '2001'
...