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

  • V. KALOSHIN (a1) and O. S. KOZLOVSKI (a2)

Abstract

In this paper we present a surprising example of a Cr unimodal map of an interval f:II whose number of periodic points Pn(f)=∣{xI: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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