COMBINATORIAL DYNAMICS AND ENTROPY IN DIMENSION ONE

• Part 1 Preliminaries: general notation; graphs, loops and cycles. Part 2 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. Part 3 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. Part 4 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.

"As a whole, the book is carefully written and contains a very detailed account of a body of material along with some new results. The book will serve as a valuable reference for those interested in the combinatorial aspects of one-dimensional dynamical systems." A Quas Mathematics Abstracts