Discrete Dynamics: Basic Theory and Examples

ISBN-13: 9783030950941 / Angielski / Miękka / 2023 / 142 str.

Andrea Bacciotti

Opis

This book offers a complete and detailed introduction to the theory of discrete dynamical systems, with special attention to stability of fixed points and periodic orbits. It provides a solid mathematical background and the essential basic knowledge for further developments such as, for instance, deterministic chaos theory, for which many other references are available (but sometimes, without an exhaustive presentation of preliminary notions). Readers will find a discussion of topics sometimes neglected in the research literature, such as a comparison between different predictions achievable by the discrete time model and the continuous time model of the same application. Another novel aspect of this book is an accurate analysis of the way a fixed point may lose stability, introducing and comparing several notions of instability: simple instability, repulsivity, and complete instability. To help the reader and to show the flexibility and potentiality of the discrete approach to dynamics, many examples, numerical simulations, and figures have been included. The book is used as a reference material for courses at a doctoral or upper undergraduate level in mathematics and theoretical engineering.

Recenzje

"The book is well written, easy to read and has many exciting examples to motivate the results. Therefore, it is a book which deserves to be read." (José S. Cánovas Peña, Mathematical Reviews, January, 2023)
"This quite small book belonging to a series entitled 'Mathematical Engineering' is a self-contained introduction to discrete- time systems. Motivated by applications arising from physics, engineering ... economics and other natural sciences, it is mainly addressed to students, aiming to show that discrete dynamics deserves its own interest and is not easy to study. ... The reviewed book can be considered ... as a preliminary study for more complete monographs ... ." (Vladimir Rasvan, zbMATH 1492.37001, 2022)

Spis treści

Discrete dynamical systems.- Stability and attraction.- Bifurcations.- Positive linear systems.

O autorze

Andrea Bacciotti was Full Professor of Mathematical Analysis at Politecnico di Torino, Italy, where he also served as Dean of the Mathematics Department. His research interests concern ordinary differential equations, differential inclusions, mathematical control theory, and switched systems theory. He is also active in popularization and diffusion of the mathematical culture. With Springer, he already published the books “Liapunov Functions and Stability in Control Theory” (ISBN 978-3-540-21332-1) and “Stability and Control of Linear Systems” (ISBN 978-3-030-02404-8).