×

zbMATH — the first resource for mathematics

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.

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
PDF BibTeX XML Cite
Full Text: DOI