{"article_type":"original","abstract":[{"text":"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.","lang":"eng"}],"publication":"Ergodic Theory and Dynamical Systems","month":"02","author":[{"first_name":"Vadim","full_name":"Kaloshin, Vadim","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628"},{"last_name":"KOZLOVSKI","full_name":"KOZLOVSKI, O. S.","first_name":"O. S."}],"quality_controlled":"1","extern":"1","date_updated":"2021-01-12T08:19:44Z","date_created":"2020-09-18T10:47:33Z","publication_identifier":{"issn":["0143-3857","1469-4417"]},"page":"159-165","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2012-02-01T00:00:00Z","volume":32,"day":"01","status":"public","publication_status":"published","issue":"1","_id":"8504","publisher":"Cambridge University Press","year":"2012","citation":{"mla":"Kaloshin, Vadim, and O. S. KOZLOVSKI. “A Cr Unimodal Map with an Arbitrary Fast Growth of the Number of Periodic Points.” <i>Ergodic Theory and Dynamical Systems</i>, vol. 32, no. 1, Cambridge University Press, 2012, pp. 159–65, doi:<a href=\"https://doi.org/10.1017/s0143385710000817\">10.1017/s0143385710000817</a>.","ama":"Kaloshin V, KOZLOVSKI OS. A Cr unimodal map with an arbitrary fast growth of the number of periodic points. <i>Ergodic Theory and Dynamical Systems</i>. 2012;32(1):159-165. doi:<a href=\"https://doi.org/10.1017/s0143385710000817\">10.1017/s0143385710000817</a>","ista":"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.","apa":"Kaloshin, V., &#38; KOZLOVSKI, O. S. (2012). A Cr unimodal map with an arbitrary fast growth of the number of periodic points. <i>Ergodic Theory and Dynamical Systems</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/s0143385710000817\">https://doi.org/10.1017/s0143385710000817</a>","short":"V. Kaloshin, O.S. KOZLOVSKI, Ergodic Theory and Dynamical Systems 32 (2012) 159–165.","chicago":"Kaloshin, Vadim, and O. S. KOZLOVSKI. “A Cr Unimodal Map with an Arbitrary Fast Growth of the Number of Periodic Points.” <i>Ergodic Theory and Dynamical Systems</i>. Cambridge University Press, 2012. <a href=\"https://doi.org/10.1017/s0143385710000817\">https://doi.org/10.1017/s0143385710000817</a>.","ieee":"V. Kaloshin and O. S. KOZLOVSKI, “A Cr unimodal map with an arbitrary fast growth of the number of periodic points,” <i>Ergodic Theory and Dynamical Systems</i>, vol. 32, no. 1. Cambridge University Press, pp. 159–165, 2012."},"type":"journal_article","article_processing_charge":"No","doi":"10.1017/s0143385710000817","title":"A Cr unimodal map with an arbitrary fast growth of the number of periodic points","oa_version":"None","keyword":["Applied Mathematics","General Mathematics"],"intvolume":"        32","language":[{"iso":"eng"}]}