Entropy and growth of expanding periodic orbits for one-dimensional maps
Fundamenta Mathematicae, Tome 157 (1998) no. 2, pp. 245-254
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
@article{10_4064_fm_157_2_3_245_254,
author = {A. Katok and A. Mezhirov},
title = {Entropy and growth of expanding periodic orbits for one-dimensional maps},
journal = {Fundamenta Mathematicae},
pages = {245--254},
publisher = {mathdoc},
volume = {157},
number = {2},
year = {1998},
doi = {10.4064/fm-157-2-3-245-254},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-157-2-3-245-254/}
}
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A. Katok; A. Mezhirov. Entropy and growth of expanding periodic orbits for one-dimensional maps. Fundamenta Mathematicae, Tome 157 (1998) no. 2, pp. 245-254. doi: 10.4064/fm-157-2-3-245-254
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