An Introduction to Dynamical Systems and Chaos

1. Front Matter

   Pages i-xviii

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2. Continuous Dynamical Systems

   • G. C. Layek

   Pages 1-35

3. Linear Systems

   • G. c. Layek

   Pages 37-82

4. Phase Plane Analysis

   • G. C. Layek

   Pages 83-127

5. Stability Theory

   • G. C. Layek

   Pages 129-158

6. Oscillations

   • G. c. Layek

   Pages 159-202

7. Theory of Bifurcations

   • G. C. Layek

   Pages 203-254

8. Hamiltonian Systems

   • G. c. Layek

   Pages 255-315

9. Symmetry Analysis

   • G. c. Layek

   Pages 317-408

10. Discrete Dynamical Systems

    • G. c. Layek

    Pages 409-439

11. Some Maps

    • G. c. Layek

    Pages 441-479

12. Conjugacy of Maps

    • G. c. Layek

    Pages 481-495

13. Chaos

    • G. c. Layek

    Pages 497-574

14. Fractals

    • G. c. Layek

    Pages 575-618

15. Back Matter

    Pages 619-622

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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.

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

“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.

• Department of Mathematics, The University of Burdwan Department of Mathematics, Burdwan, India

  G.C. Layek

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.

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