Introduction to applied nonlinear dynamical systems and chaos. 2nd ed.

*(English)*Zbl 1027.37002
Texts in Applied Mathematics. 2. New York, NY: Springer. xix, 843 p. (2003).

The book is written by the famous scientist in the area of ordinary differential equations. It presents a systematic treatment of the theory of dynamical systems and invariant manifolds.

This book is intended for advanced undergraduate and graduate students as an introduction to applied nonlinear dynamics and chaos. The author has placed emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about the behavior of these systems. He has included the basic core material that is necessary for higher levels of study and research. Thus, people who do not necessarily have an extensive mathematical background, such as students in engineering, physics, chemistry, and biology, will find this text as useful as will students of mathematics.

This new edition contains extensive new material on invariant manifold theory and normal forms (in particular, Hamiltonian normal forms and the role of symmetry), Lagrangian, Hamiltonian, gradient, and reversible dynamical systems are also discussed. Elementary Hamiltonian bifurcations are covered, as well as the basic properties of circle maps. The book contains an extensive bibliography as well as a detailed glossary of terms, making it a comprehensive book on applied nonlinear dynamical systems from a geometrical and analytical point of view.

The book is well written and contains a number of examples and exercises.

For a review of the original (1990) see Zbl 0701.58001.

This book is intended for advanced undergraduate and graduate students as an introduction to applied nonlinear dynamics and chaos. The author has placed emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about the behavior of these systems. He has included the basic core material that is necessary for higher levels of study and research. Thus, people who do not necessarily have an extensive mathematical background, such as students in engineering, physics, chemistry, and biology, will find this text as useful as will students of mathematics.

This new edition contains extensive new material on invariant manifold theory and normal forms (in particular, Hamiltonian normal forms and the role of symmetry), Lagrangian, Hamiltonian, gradient, and reversible dynamical systems are also discussed. Elementary Hamiltonian bifurcations are covered, as well as the basic properties of circle maps. The book contains an extensive bibliography as well as a detailed glossary of terms, making it a comprehensive book on applied nonlinear dynamical systems from a geometrical and analytical point of view.

The book is well written and contains a number of examples and exercises.

For a review of the original (1990) see Zbl 0701.58001.

Reviewer: Alexander Olegovich Ignatyev (Donetsk)

##### MSC:

37-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory |

37C20 | Generic properties, structural stability of dynamical systems |

37D10 | Invariant manifold theory for dynamical systems |

34C28 | Complex behavior and chaotic systems of ordinary differential equations |

37G05 | Normal forms for dynamical systems |

37E10 | Dynamical systems involving maps of the circle |

37J15 | Symmetries, invariants, invariant manifolds, momentum maps, reduction (MSC2010) |

37J20 | Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems |

37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |

34-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations |

70-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of particles and systems |