An Introduction to Dynamical Systems and Chaos

G.C. Layek (Autor)

Buch | Softcover

622 Seiten

2019 | Softcover reprint of the original 1st ed. 2015
Springer, India, Private Ltd (Verlag)
978-81-322-3794-5 (ISBN)

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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.

G. C. LAYEK is professor at the Department of Mathematics, The University of Burdwan, India. He obtained his PhD degree from Indian Institute of Technology Kharagpur and did his postdoctoral studies at Indian Statistical Institute, Kolkata. His areas of research are theoretical fluid dynamics of viscous fluid, fluid turbulence and chaotic systems. Professor Layek has published several research papers in international journals of repute and has visited several international universities including Saint Petersburg State University, Kazan State Technological University, Russia, for collaborative research work and teaching.

Continuous Dynamical Systems.- Linear Systems.- Phase Plane Analysis.- Stability Theory.- Oscillations.- Theory of Bifurcations.- Hamiltonian Systems.- Symmetry Analysis.- Discrete Dynamical Systems.- Some Maps.- Conjugacy of Maps.- Chaos.- Fractals.

Erscheinungsdatum	19.12.2018
Zusatzinfo	222 Illustrations, color; XVIII, 622 p. 222 illus. in color.
Verlagsort	New Delhi
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Bifurcation Theory • chaos theory • Conjugacy • Flows • Fractals. • Hamiltonian Flows • Lie Symmetry Analysis • oscillations • phase plane analysis • Sability Theory
ISBN-10	81-322-3794-3 / 8132237943
ISBN-13	978-81-322-3794-5 / 9788132237945
Zustand	Neuware