Differential Equations and Dynamical Systems

Lawrence Perko

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English

Springer Verlag
01 June 2006

Mathematics & Sciences; Differential calculus & equations; Integral calculus & equations; Fluid mechanics; Flow, turbulence, rheology

Series: Texts in Applied Mathematics

This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem, the use of the Poincare map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles. In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise's algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems.

By: Lawrence Perko
Imprint: Springer Verlag
Country of Publication: United States
Edition: 3rd Revised edition
Volume: v. 7
Dimensions: Height: 235mm, Width: 155mm, Spine: 31mm
Weight: 2.160kg
ISBN: 9780387951164
ISBN 10: 0387951164
Series: Texts in Applied Mathematics
Pages: 567
Publication Date: 01 June 2006
Audience: College/higher education , Professional and scholarly , Further / Higher Education , Undergraduate
Format: Hardback
Publisher's Status: Active

Series Preface.- Preface to the Third Edition.- Linear Systems.- Nonlinear Systems: Local Theory.- Nonlinear Systems: Global Theory.- Nonlinear Systems: Bifurcation Theory.- References.- Additional References.- Index.

Reviews for Differential Equations and Dynamical Systems

Reviews from the first edition: ...The text succeeds admiraby ... Examples abound, figures are used to advantage, and a reasonable balance is maintained between what is proved in detail and what is asserted with supporting references ... Each section closes with a set of problems, many of which are quite interesting and round out the text material ... this book is to be highly recommended both for use as a text, and for professionals in other fields wanting to gain insight into modern aspects of the geometric theory of continuous (i.e., not discrete) dynamical systems. MATHEMATICAL REVIEWS