Dynamical Systems by Example

​Luís Barreira is professor of mathematics at the University of Lisbon. His main research interests are in dynamical systems and ergodic theory. Prof. Barreira has authored several books published with Springer including Lyapunov Exponents, Thermodynamic Formalism and Applications to Dimension Theory (PM), (with C. Valls) Dynamical Systems (UTX) and Stability of Nonautonomous Differential Equations (LNM), (with C.  Valls and D. Dragicevic) Admissibility and Hyperbolicity (SBM).Claudia Valls is professor of mathematics at the University of Lisbon. Her main research interest is in dynamical systems. Prof. Valls has authored several books published with Springer including (with L. Barreira) Dynamical Systems (UTX) and Stability of Nonautonomous Differential Equations (LNM), and (with L. Barreira and D. Dragicevic) Admissibility and Hyperbolicity (SBM).

• Part I. Theory and Problems.- I.1 Basic Theory.- I.2 Topological Dynamics.- I.3 Low-Dimensional Dynamics.- I.4 Hyperbolic Dynamics.- I.5 Symbolic Dynamics.- I.6 Ergodic Theory.- Part II. Problems and Solutions.- II.1 Basic Theory.- II.2 Topological Dynamics.- II.3 Low-Dimensional Dynamics.- II.4 Hyperbolic Dynamics.- II.5 Symbolic Dynamics.- II.6 Ergodic Theory.- References.- Index.

“This is a really nice problem book on the subject covering a large body of subjects … . All problems are presented with proper context (including definitions and relevant theorems) together with complete solutions. All solutions are provided with sufficient details such that the book is not only suitable for teachers but also for students who are looking for solved examples to better understand abstract topics. In summary, this is a most welcome addition to the present literature” (G. Teschl, Monatshefte für Mathematik, Vol. 196 (1), 2021)“The book under review represents a great help for anyone who wants to study the theory of dynamical systems. … The book is very well written and may be also very useful for mathematicians teaching courses on dynamical systems.” (Krzysztof Ciesielski, Mathematical Reviews, September, 2020)“It would quickly provide students with a good set of problems and an introduction to a good range of concepts and issues relevant to dynamics. The book could also be a valuable resource for individual study … . anyone lecturing on dynamical systems, who would find here an excellent and diverse selection of problems, carefully assembled and usefully ‘scaffolded’ in the educational terminology. I enjoyed it, and recommend it highly.” (Thomas B. Ward, zbMATH 1421.37001, 2019)