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An Introduction to Dynamical Systems and Chaos [electronic resource] / by G.C. Layek

Author
Layek, G.C.
Published
New Delhi : Springer India : Imprint: Springer, 2015.
Edition
1st ed. 2015.
Physical Description
XVIII, 622 p. 222 illus. in color. online resource
Additional Creators
SpringerLink (Online service)
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Contents
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.
Summary
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.
Subject(s)
ISBN
9788132225560
Digital File Characteristics
text file PDF
Note
AVAILABLE ONLINE TO AUTHORIZED PSU USERS.
Part Of
Springer eBooks
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