Overview
- Discusses scaling investigation in nonlinear dynamics
- Applies the scaling formalism to discuss bifurcations and diffusion
- Discusses transition from limited to unlimited diffusion that may also be applied to diffusion in energy, which is a hot topic investigated in billiard dynamics.
- Can be used as textbook and reference book in mathematics, physics, mechanical and control engineering
Part of the book series: Nonlinear Physical Science (NPS)
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Table of contents (15 chapters)
Keywords
About this book
From the variation of control parameters, physical observables in the phase space may be characterized by using power laws that many times yield into universal behavior. The application of such a formalism has been well accepted in the scientific community of nonlinear dynamics. Therefore I had in mind when writing this book was to bring together few of the research results in nonlinear systems using scaling formalism that could treated either in under-graduation as well as in the post graduation in the several exact programs but no earlier requirements were needed from the students unless the basic physics and mathematics. At the same time, the book must be original enough to contribute to the existing literature but with no excessive superposition of the topics already dealt with in other text books. The majority of the Chapters present a list of exercises. Some of them are analytic and others are numeric with few presenting some degree of computational complexity.
Reviews
“The titles of the chapters are quite informative and they reflect not only the structure of the book but also its content ... . The book provides useful introductory materials, including exercises, for undergraduate and graduate students who wish to have an overview of common scaling properties at their related methodologies in mathematics, physics, mechanical and control engineering.” (Vladimir Sobolev, zbMATH 1483.37002, 2022)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Scaling Laws in Dynamical Systems
Authors: Edson Denis Leonel
Series Title: Nonlinear Physical Science
DOI: https://doi.org/10.1007/978-981-16-3544-1
Publisher: Springer Singapore
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Higher Education Press 2021
Hardcover ISBN: 978-981-16-3543-4Published: 27 August 2021
Softcover ISBN: 978-981-16-3546-5Published: 28 August 2022
eBook ISBN: 978-981-16-3544-1Published: 26 August 2021
Series ISSN: 1867-8440
Series E-ISSN: 1867-8459
Edition Number: 1
Number of Pages: XXVII, 247
Number of Illustrations: 30 b/w illustrations, 79 illustrations in colour
Topics: Dynamical Systems and Ergodic Theory, Vibration, Dynamical Systems, Control, Phase Transitions and Multiphase Systems