Differential Equations and Dynamical Systems (Texts in Applied Mathematics)

Lawrence Perko

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Book by Perko Lawrence

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This book contains a systematic study of autonomous systems of ordinary differential equations and dynamical systems. It begins with a thorough treatment of linear systems; however, the main topic of the book is local and global behavior of nonlinear systems. The main purpose of the book is to introduce students to the qualitative and geometric theory of ordinary differential equations originated by at the end of the 19th century. It is also intended as a reference book for mathematicians doing research on dynamical systems. There are several new features in this book such as the simplified proof of the Hartman-Grobman Theorem and examples illustrating the proof, map in the theory of limit cycles, an efficient method for obtaining the global phase portrait of two-dimensional systems, and the description of the behavior of a one-parameter family of limit cycles. Readers of this book will find that, except for certain topics of current mathematical research such as the number of limit cycles and the nature of attracting sets of dynamical systems, the global qualitative theory of a nonlinear dynamical system leads to an understanding of the solution set of the nonlinear system that rivals the understanding what we have of linear flows.

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.

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1.Differential Equations and Dynamical Systems (Texts in Applied Mathematics)

Editorial: Springer 1993-08-20 (1993)
ISBN 10: 0387974431 ISBN 13: 9780387974439
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Book Services Plus, Inc.
(Oakland Park, FL, Estados Unidos de America)
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Descripción Springer 1993-08-20, 1993. Hardcover. Estado de conservación: New. 1st ed. 1991. Corr.. 0387974431 Looks like new. Clean text. SATISF GNTD + SHIPS W/IN 24 HRS. Sorry, no APO deliveries. Ships in a padded envelope with free tracking. P30E. Nº de ref. de la librería 800154933

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2.Differential Equations and Dynamical Systems (Texts in Applied Mathematics)

Editorial: Springer (1993)
ISBN 10: 0387974431 ISBN 13: 9780387974439
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Murray Media
(North Miami Beach, FL, Estados Unidos de America)
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Descripción Springer, 1993. Hardcover. Estado de conservación: New. Nº de ref. de la librería P110387974431

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3.Differential Equations and Dynamical Systems (Texts in Applied Mathematics)

Editorial: Springer (1990)
ISBN 10: 0387974431 ISBN 13: 9780387974439
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Descripción Springer, 1990. Hardcover. Estado de conservación: New. This item is printed on demand. Nº de ref. de la librería DADAX0387974431

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4.Differential Equations and Dynamical Systems (Texts in Applied Mathematics)

Editorial: Springer (1990)
ISBN 10: 0387974431 ISBN 13: 9780387974439
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Irish Booksellers
(Rumford, ME, Estados Unidos de America)
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Descripción Springer, 1990. Hardcover. Estado de conservación: New. book. Nº de ref. de la librería 387974431

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5.Differential Equations and Dynamical Systems (Texts in Applied Mathematics)

Editorial: Springer (1993)
ISBN 10: 0387974431 ISBN 13: 9780387974439
Librería
Irish Booksellers
(Rumford, ME, Estados Unidos de America)
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Descripción Springer, 1993. Hardcover. Estado de conservación: New. book. Nº de ref. de la librería 0387974431

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6.Differential Equations and Dynamical Systems (Texts in Applied Mathematics)

Editorial: Springer (1993)
ISBN 10: 0387974431 ISBN 13: 9780387974439