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Nonlinear Differential Equations and Dynamical Systems Paperback - 1996
by Ferdinand Verhulst
From the rear cover
On the subject of differential equations many elementary books have been written. This book bridges the gap between elementary courses and research literature. The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed first. Stability theory is then developed starting with linearisation methods going back to Lyapunov and Poincar. In the last four chapters more advanced topics like relaxation oscillations, bifurcation theory, chaos in mappings and differential equations, Hamiltonian systems are introduced, leading up to the frontiers of current research: thus the reader can start to work on open research problems, after studying this book. This new edition contains an extensive analysis of fractal sets with dynamical aspects like the correlation- and information dimension. In Hamiltonian systems, topics like Birkhoff normal forms and the Poincar-Birkhoff theorem on periodicsolutions have been added. There are now 6 appendices with new material on invariant manifolds, bifurcation of strongly nonlinear self-excited systems and normal forms of Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, and is illustrated by many examples.
Details
- Title Nonlinear Differential Equations and Dynamical Systems
- Author Ferdinand Verhulst
- Binding Paperback
- Edition 2 REV SUB
- Pages 306
- Volumes 1
- Language ENG
- Publisher Springer
- Date 1996-09-06
- Illustrated Yes
- Features Illustrated, Maps
- ISBN 9783540609346 / 3540609342
- Weight 1.12 lbs (0.51 kg)
- Dimensions 9.19 x 6.09 x 0.74 in (23.34 x 15.47 x 1.88 cm)
- Library of Congress Catalog Number 96002740
- Dewey Decimal Code 515.355
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Springer Verlag, 1997. Paperback. New. 2nd revised subsequent edition. 303 pages. German language. 9.50x6.25x0.75 inches.
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Paperback / softback. New. For lecture courses that cover the classical theory of nonlinear differential equations associated with Poincare and Lyapunov and introduce the student to the ideas of bifurcation theory and chaos, this text is ideal.
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