A C-r unimodal map with an arbitrary fast growth of the number of periodic points

作者：Kaloshin V^*; Kozlovski O S

来源：Ergodic Theory and Dynamical Systems, 2012, 32: 159-165.

DOI：10.1017/S0143385710000817

In this paper we present a surprising example of a C-r unimodal map of an interval f : I -%26gt; 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 %26apos;non-flatness%26apos; 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.

• 出版日期2012-2