Topics from One-Dimensional Dynamics
The book introduces the reader to a large number of basic dynamical concepts, including topological dynamics (transitivity, recurrence, topological conjugacy, entropy), measurable dynamics (Poincaré recurrence, ergodicity), symbolic dynamics and quadratic complex dynamics (Julia and Fatou sets and the Mandelbrot set). Developments of advanced combinatoric tools (Hofbauer towers, kneading maps) and in number theory (Farey trees, continued fractions) are used to give a more detailed description of the dynamics of several classes of 1d maps, including unimodal and tent maps, circle maps, rigid rotations and β-transformations. Simpler results are often presented in the form of exercises, hence the book is particularly useful for students/beginners in the field. Due to an extensive bibliography, it will also serve as a very good reference book.