Nonlinear Differential Equations and Dynamical Systems
PAYBACK Punkte
23 °P sammeln!
"A good book for a nice price!"Monatshefte für Mathematik"... for lecture courses that cover the classical theory of nonlinear differential equations associated with Poincaré and Lyapunov and introduce the student to the ideas of bifurcation theory and chaos Äthis isÜ an ideal text ..."Mathematika"The pedagogical style is excellent, consisting typically of an insightful overview followed by theorems, illustrative examples and exercises"Choice
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 Poincaré. 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 Poincaré-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.
Andere Kunden interessierten sich für
