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A Cr unimodal map with an arbitrary fast growth of the number of periodic points
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Kaloshin, V. and Kozlovski, O. (2012) A Cr unimodal map with an arbitrary fast growth of the number of periodic points. Ergodic Theory and Dynamical Systems, Vol.32 (No.1). pp. 159-165. doi:10.1017/S0143385710000817 ISSN 0143-3857.
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Official URL: http://dx.doi.org/10.1017/S0143385710000817
Abstract
In this paper we present a surprising example of a C(r) unimodal map of an interval f : I -> I whose number of periodic points P(n)(f) = vertical bar{x is an element of I : f(n) x = x}vertical bar grows faster than any ahead given sequence along a subsequence (n)k = 3(k). This example also shows that 'non-flatness' of critical points is necessary for the Martens de Melo van Strien theorem [M. Martens, W. de Melo and S. van Strien. Julia-Fatou-Sullivan theory for real one-dimensional dynamics. Acta Math. 168(3-4) (1992), 273-318] to hold.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Mappings (Mathematics) | ||||
Journal or Publication Title: | Ergodic Theory and Dynamical Systems | ||||
Publisher: | Cambridge University Press | ||||
ISSN: | 0143-3857 | ||||
Official Date: | February 2012 | ||||
Dates: |
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Volume: | Vol.32 | ||||
Number: | No.1 | ||||
Page Range: | pp. 159-165 | ||||
DOI: | 10.1017/S0143385710000817 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 19 December 2015 | ||||
Date of first compliant Open Access: | 19 December 2015 | ||||
Funder: | American Institute of Mathematics (AIM) |
Data sourced from Thomson Reuters' Web of Knowledge
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