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Kaloshin, V.; Kozlovski, O. (2012)
Publisher: Cambridge University Press
Languages: English
Types: Article
Subjects: QA
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.
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