A Cr unimodal map with an arbitrary fast growth of the number of periodic points

V. Kaloshin, O.S. KOZLOVSKI, Ergodic Theory and Dynamical Systems 32 (2012) 159–165.

Download
No fulltext has been uploaded. References only!

Journal Article | Published | English
Author
Kaloshin, VadimIST Austria; 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.
Publishing Year
Date Published
2012-02-01
Journal Title
Ergodic Theory and Dynamical Systems
Volume
32
Issue
1
Page
159-165
IST-REx-ID

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, 32(1), 159–165. 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 32, no. 1 (2012): 159–65. 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, 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.

Export

Marked Publications

Open Data IST Research Explorer

Search this title in

Google Scholar