Combinatorial Dynamics and Entropy in Dimension One
Combinatorial Dynamics and Entropy in Dimension One
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DOI：
10.1142/1980
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发表时间：
2000-11
期刊：
影响因子：
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通讯作者：
L. Alsedà;J. Llibre;M. Misiurewicz
中科院分区：
文献类型：
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作者：
L. Alsedà;J. Llibre;M. Misiurewicz
预备知识：一般符号、图、环与圈。区间映射：沙可夫斯基定理、具有规定周期集的映射、区间映射的强制关系模式、强制关系的反对称性、P -单调映射与定向模式、定理2.6.13的推论、模式与周期的稳定性、本原模式、扩张、本原定向模式的刻画、关于本原定向模式的更多内容。圆映射：圆映射的提升与度、提升的圈、圈与提升的圈、度不同于 -1、0和1的映射的周期、度为0的映射的周期、度为 -1的映射的周期、旋转数与扭转、提升的圈、旋转区间的估计、度为1的映射的周期、具有规定周期集的度为1的映射、其他结果。附录：提升的模式。熵：定义、区间映射的熵、马蹄、圈的熵、熵的连续性性质、到常斜率映射的半共轭、圆映射的熵、定理4.7.3的证明
Preliminaries: general notation graphs, loops and cycles. Interval maps: the Sharkovskii Theorem maps with the prescribed set of periods forcing relation patterns for interval maps antisymmetry of the forcing relation P-monotone maps and oriented patterns consequences of Theorem 2.6.13 stability of patterns and periods primary patterns extensions characterization of primary oriented patterns more about primary oriented patterns. Circle maps: liftings and degree of circle maps lifted cycles cycles and lifted cycles periods for maps of degree different from -1, 0 and 1 periods for maps of degree 0 periods for maps of degree -1 rotation numbers and twist lifted cycles estimate of a rotation interval periods for maps of degree 1 maps of degree 1 with the prescribed set of periods other results. Appendix: lifted patterns. Entropy: definitions entropy for interval maps horseshoes entropy of cycles continuity properties of the entropy semiconjugacy to a map of a constant slope entropy for circle maps proof of Theorem 4.7.3.