COMBINATORIAL DYNAMICS AND ENTROPY IN DIMENSION ONE (2ND EDITION)

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.