Overview
- Authors are among the leaders in their field and well-known expositors
- Includes instruction manual and examples for the free software P4 (for numerical experiments on differential equations) available online
- Very different treatment, at somewhat higher level, from numerous other textbooks on the subject
Part of the book series: Universitext (UTX)
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Keywords
Table of contents (10 chapters)
Reviews
From the reviews:
"Qualitative Theory of Planar Differential Systems is a graduate-level introduction to systems of polynomial autonomous differential equations in two real variables. … This text treats the basic results of the qualitative theory with competence and clarity. … the material of the text is well-integrated and readily accessible to graduate students or especially capable advanced undergraduates." (William J. Satzer, MathDL, December, 2006)
"This textbook, written by well-known scientists in the field of the qualitative theory of ordinary differential equations, presents a comprehensive introduction to fundamental and essential topics of real planar differential autonomous systems. … The emphasis is mainly qualitative, although attention is also given to more algebraic aspects. There is an extensive list of references. The monograph is well written and contains a lot of illustrations and examples. It will be useful for students, teachers and researchers." (Alexander Grin, Zentralblatt MATH, Vol. 1110 (12), 2007)
"The planar differential systems which are the subject of this book are systems of autonomous differential equations … . This book contains a wealth of information and techniques, some of it unavailable outside the research literature. … Moreover the exposition is accurate, clear, and well-motivated. … this work could serve well both as a textbook for a course in smooth dynamical systems on planar regions, and as a reference in which important tools of current research are thoroughly explained and their use illustrated." (Douglas S. Shafer, Mathematical Reviews, Issue 2007 f)
Authors and Affiliations
About the authors
FREDDY DUMORTIER is full professor at Hasselt University (Belgium), and a member of the Royal Flemish Academy of Belgium for Science and the Arts. He was a long-term visitor at different important universities and research institutes. He is the author of many papers and his main results deal with singularities and their unfolding, singular perturbations, Lienard equations and Hilbert’s 16th problem.
JAUME LLIBRE is full professor at the Autonomous University of Barcelona (Spain), he is a member of the Royal Academy of Sciences and Arts of Barcelona. He was a long term visitor at different important universities and research institutes. He is the author of many papers and had a large number of Ph. D. students. His main results deal with periodic orbits, topological entropy, polynomial vector fields, Hamiltonian systems and celestial mechanics.
JOAN C. ARTES is professor at the Autonomous University of Barcelona (Spain). His main results deal with polynomial vector fields, more concretely quadratic ones. He programmed, some 20 years ago, the first version of P4 (only for quadratic systems) from which the program P4 was developed with the help of Chris Herssens and Peter De Maesschalck.
Bibliographic Information
Book Title: Qualitative Theory of Planar Differential Systems
Authors: Freddy Dumortier, Jaume Llibre, Joan C. Artés
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-540-32902-2
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2006
Softcover ISBN: 978-3-540-32893-3Published: 06 September 2006
eBook ISBN: 978-3-540-32902-2Published: 13 October 2006
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XVI, 302
Topics: Ordinary Differential Equations, Dynamical Systems and Ergodic Theory