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＜E-Book＞
Differential Equations and Dynamical Systems / by Lawrence Perko
(Texts in Applied Mathematics. ISSN:21969949 ; 7)

Edition	3rd ed. 2001.
Publisher	(New York, NY : Springer New York : Imprint: Springer)
Year	2001
Language	English
Size	XIV, 557 p. 11 illus : online resource
Authors	*Perko, Lawrence author SpringerLink (Online service)
Subjects	LCSH:Mathematical analysis LCSH:Continuum mechanics LCSH:Mechanics FREE:Analysis FREE:Continuum Mechanics FREE:Classical Mechanics
Notes	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 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 contains materials on higher order Melnikov functions 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 HTTP:URL=https://doi.org/10.1007/978-1-4613-0003-8

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