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 language | English (US) |
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Pages (from-to) | 245-254 |
Number of pages | 10 |
Journal | Fundamenta Mathematicae |
Volume | 157 |
Issue number | 2-3 |
State | Published - 1998 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory