Entropy and growth of expanding periodic orbits for one-dimensional maps

A. Katok, A. Mezhirov

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Let f be a continuous map of the circle S1 or the interval I into itself, piecewise C1 piecewise monotone with finitely many intervals of monotonicity and having positive entropy h. For any ε > 0 we prove the existence of at least e (h-ε)nk periodic points of period nk with large derivative along the period, |(fnk) ′'| > e (h-ε)nk for some subsequence {nk} of natural numbers. For a strictly monotone map f without critical points we show the existence of at least (1 - ε)ehn such points.

Original languageEnglish (US)
Pages (from-to)245-254
Number of pages10
JournalFundamenta Mathematicae
Volume157
Issue number2-3
StatePublished - 1998

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Fingerprint

Dive into the research topics of 'Entropy and growth of expanding periodic orbits for one-dimensional maps'. Together they form a unique fingerprint.

Cite this