An Introduction to Dynamical Systems and Chaos
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Beschreibung
The book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems and chaos theory. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, and a number of examples worked out in detail and exercises have been included. Chapters 1–8 are devoted to continuous systems, beginning with one-dimensional flows. Symmetry is an inherent character of nonlinear systems, and the Lie invariance principle and its algorithm for finding symmetries of a system are discussed in Chap. 8. Chapters 9–13 focus on discrete systems, chaos and fractals. Conjugacy relationship among maps and its properties are described with proofs. Chaos theory and its connection with fractals, Hamiltonianflows and symmetries of nonlinear systems are among the main focuses of this book.
Over the past few decades, there has been an unprecedented interest and advances in nonlinear systems, chaos theory and fractals, which is reflected in undergraduate and postgraduate curricula around the world. The book is useful for courses in dynamical systems and chaos, nonlinear dynamics, etc., for advanced undergraduate and postgraduate students in mathematics, physics and engineering.
The book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems and chaos theory. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, and a number of examples worked out in detail and exercises have been included. Chapters 1–8 are devoted to continuous systems, beginning with one-dimensional flows. Symmetry is an inherent character of nonlinear systems, and the Lie invariance principle and its algorithm for finding symmetries of a system are discussed in Chap. 8. Chapters 9–13 focus on discrete systems, chaos and fractals. Conjugacy relationship among maps and its properties are described with proofs. Chaos theory and its connection with fractals, Hamiltonian flows and symmetries of nonlinear systems are among the main focuses of this book. Over the past few decades, there has been an unprecedented interest and advances in nonlinear systems, chaos theory and fractals, which is reflected in undergraduate and postgraduate curricula around the world. The book is useful for courses in dynamical systems and chaos, nonlinear dynamics, etc., for advanced undergraduate and postgraduate students in mathematics, physics and engineering.
Presents a comprehensive overview of nonlinear dynamics Discusses continuous and discrete systems by using a systematic, sequential, and logical approach Presents numerous solved examples with physical explanations of oscillations, bifurcations, and Lie symmetry analysis of nonlinear systems Explains conjugacy, chaos, and fractals in detail Is useful to students of mathematics, physics, and engineering Includes supplementary material: sn.pub/extras
Autor*in
G.C. Layek
Themen in »An Introduction to Dynamical Systems and Chaos«
Bifurcation Theory Chaos Theory Conjugacy Flows Fractals. Hamiltonian Flows Lie Symmetry Analysis Oscillations Phase Plane Analysis Sability Theory
Stimmen zu »An Introduction to Dynamical Systems and Chaos«
“The text is a strong and rigorous treatment of the introduction of dynamical systems … . The exercises presented at the end of each chapter are suitable for upper-level undergraduates and graduate students. As a reference source, the text is very well-organized with its division of the subject into continuous and discrete dynamical systems. Summing Up: Recommended. Upper-division undergraduates through professionals and practitioners.” (M. D. Sanford, Choice, Vol. 54 (2), October, 2016)
This textbook provides a clear presentation of many standard topics in dynamical systems. Overall, the book is well written in a clear logical manner. The chapter titles precisely indicate the topics covered by the author. These are…..
s="" are="" used="" in="" study="" of="" continuous="" discrete="" dynamical="" systems.="" due="" to="" combination="" a="" careful="" development="" theory,="" many="" worked="" example="" problems,="" variety="" applications,="" well-chosen="" exercises, An introduction to dynamical systems and chaos is very well suited as either a course text or for self-study by students. The book could also serve as a nice supplement to many of the other standard texts on dynamical systems.
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