# An Introduction to Dynamical Systems and Chaos

• 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

Textbook

1. Front Matter
Pages i-xviii
2. G. C. Layek
Pages 1-35
3. G. c. Layek
Pages 37-82
4. G. C. Layek
Pages 83-127
5. G. C. Layek
Pages 129-158
6. G. c. Layek
Pages 159-202
7. G. C. Layek
Pages 203-254
8. G. c. Layek
Pages 255-315
9. G. c. Layek
Pages 317-408
10. G. c. Layek
Pages 409-439
11. G. c. Layek
Pages 441-479
12. G. c. Layek
Pages 481-495
13. G. c. Layek
Pages 497-574
14. G. c. Layek
Pages 575-618
15. Back Matter
Pages 619-622

### Introduction

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.

### Keywords

Bifurcation Theory Chaos Theory Conjugacy Flows Fractals. Hamiltonian Flows Lie Symmetry Analysis Oscillations Phase Plane Analysis Sability Theory

#### Authors and affiliations

1. 1.Department of MathematicsThe University of Burdwan Department of MathematicsBurdwanIndia

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.

### Bibliographic information

• Book Title An Introduction to Dynamical Systems and Chaos
• Authors G.C. Layek
• DOI https://doi.org/10.1007/978-81-322-2556-0
• Copyright Information Springer India 2015
• Publisher Name Springer, New Delhi
• eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
• Hardcover ISBN 978-81-322-2555-3
• Softcover ISBN 978-81-322-3794-5
• eBook ISBN 978-81-322-2556-0
• Edition Number 1
• Number of Pages XVIII, 622
• Number of Illustrations 0 b/w illustrations, 222 illustrations in colour
• Topics
• Buy this book on publisher's site
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