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An Introduction to Dynamical Systems and Chaos

  • G.C. Layek

Table of contents

  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

About this book

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

  • G.C. Layek
    • 1
  1. 1.Department of MathematicsThe University of Burdwan Department of MathematicsBurdwanIndia

Bibliographic information

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