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Book synopsis

This book bridges the gap between elementary courses and the research literature. The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed.§Stability theory is developed starting with linearisation methods going back to Lyapunov and Poincar. The global direct method is then discussed. To obtain more quantitative information the Poincar -Lindstedt method is introduced to approximate periodic solutions while at the same time proving existence by the implicit function theorem. The method of averaging is introduced as a general approximation-normalisation method.§The last four chapters introduce the relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, Hamiltonian systems (recurrence, invariant tori, periodic solutions).

Book details

Book category Books in English Mathematics & science Mathematics Calculus & mathematical analysis

• Full title: Nonlinear Differential Equations and Dynamical Systems
• Author: Ferdinand Verhulst
• Language: English
• Binding: Paperback
• Number of pages: 306
• EAN: 9783540609346
• ISBN: 3540609342
• ID: 01566100
• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Weight: 492 g
• Dimensions: 233 × 157 × 17 mm
• Date of publishing: 06. September 1996

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