Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

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

100%

Katok A., Mezhirov A.

Fundamenta Mathematicae

1998

tom 157

nr 2-3

245-254

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

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Katok A.

1 Mezhirov A.

1 1998

Wyniki wyszukiwania

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