Differential Equations and Dynamical Systems

3rd Auflage 2001. Softcover Nachdruck of the original 3rd Auflage 2001
ISBN: 978-1-4612-6526-9
Verlag: Springer

Buch, Englisch, Band 7, 557 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 861 g

Reihe: Texts in Applied Mathematics

This textbook, ideal for students and lecturers alike, is nothing less than 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. 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.

Zielgruppe

Graduate

Autoren/Hrsg.

Perko, Lawrence

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme

Inhaltsverzeichnis

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.