Combinatorial Dynamics and Entropy in Dimension One 论文

摘要

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.