Lawrence Perko

Differential Equations and Dynamical Systems (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 557
• Erscheinungstermin: 21. November 2013
• Englisch
• ISBN-13: 9781461300038
• Artikelnr.: 44043608

Autorenporträt

Lawrence Perko, Northern Arizona University, Flagstaff, AZ, USA

Inhaltsangabe

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.

Rezensionen

Rezensions from the first edition: "The text succeeds admirably. 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

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