A Cr unimodal map with an arbitrary fast growth of the number of periodic points
Kaloshin V, KOZLOVSKI OS. 2012. A Cr unimodal map with an arbitrary fast growth of the number of periodic points. Ergodic Theory and Dynamical Systems. 32(1), 159–165.
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Journal Article
| Published
| English
Author
Kaloshin, VadimISTA 
;
KOZLOVSKI, O. S.
;
KOZLOVSKI, O. S.Abstract
In this paper we present a surprising example of a Cr unimodal map of an interval f:I→I whose number of periodic points Pn(f)=∣{x∈I:fnx=x}∣ grows faster than any ahead given sequence along a subsequence nk=3k. 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.
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Publishing Year
Date Published
2012-02-01
Journal Title
Ergodic Theory and Dynamical Systems
Publisher
Cambridge University Press
Volume
32
Issue
1
Page
159-165
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Cite this
Kaloshin V, KOZLOVSKI OS. A Cr unimodal map with an arbitrary fast growth of the number of periodic points. Ergodic Theory and Dynamical Systems. 2012;32(1):159-165. doi:10.1017/s0143385710000817
Kaloshin, V., & KOZLOVSKI, O. S. (2012). A Cr unimodal map with an arbitrary fast growth of the number of periodic points. Ergodic Theory and Dynamical Systems. Cambridge University Press. https://doi.org/10.1017/s0143385710000817
Kaloshin, Vadim, and O. S. KOZLOVSKI. “A Cr Unimodal Map with an Arbitrary Fast Growth of the Number of Periodic Points.” Ergodic Theory and Dynamical Systems. Cambridge University Press, 2012. https://doi.org/10.1017/s0143385710000817.
V. Kaloshin and O. S. KOZLOVSKI, “A Cr unimodal map with an arbitrary fast growth of the number of periodic points,” Ergodic Theory and Dynamical Systems, vol. 32, no. 1. Cambridge University Press, pp. 159–165, 2012.
Kaloshin V, KOZLOVSKI OS. 2012. A Cr unimodal map with an arbitrary fast growth of the number of periodic points. Ergodic Theory and Dynamical Systems. 32(1), 159–165.
Kaloshin, Vadim, and O. S. KOZLOVSKI. “A Cr Unimodal Map with an Arbitrary Fast Growth of the Number of Periodic Points.” Ergodic Theory and Dynamical Systems, vol. 32, no. 1, Cambridge University Press, 2012, pp. 159–65, doi:10.1017/s0143385710000817.
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