Fundamentals of Dynamical Systems and Bifurcation Theory.

Medved, Milan:

ISBN 10: 0750301503 / ISBN 13: 9780750301503

Editore: Institute of Physics Publishing, 1992

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Zust: Gutes Exemplar. 308 Seiten Englisch 678g.

Codice articolo 484319

Dati bibliografici

• Titolo: Fundamentals of Dynamical Systems and Bifurcation Theory.
• Editore: Institute of Physics Publishing
• Data di pubblicazione: 1992
• Lingua: Inglese
• ISBN 10: 0750301503
• ISBN 13: 9780750301503
• Rilegatura: Karton
• Condizione: Sehr gut
• Peso: 678 grammi
• Cataloghi dei venditori:
  • Mathematik

Descrizione articolo

Riassunto

This graduate level text explains the fundamentals of the theory of dynamical systems. After reading it you will have a good enough understanding of the area to study the extensive literature on dynamical systems. The book is self contained, as all the essential definitions and proofs are supplied, as are useful references: all the reader needs is a knowledge of basic mathematical analysis, algebra and topology. However, the first chapter contains an explanation of some of the methods of differential topology an understanding of which is essential to the theory of dynamical systems. A clear introduction to the field, which is equally useful for postgraduates in the natural sciences, engineering and economics.

Contenuti

Selected reading on foundations of algebra, topology, mathematical analysis and theory of differential equations: Some basic concepts and notations. Relations on a set. Linear, euclidean and linear normed spaces. Metric spaces. Topological spaces. Matrices. Linear mappings. Mathematical analysis. Differential equations. Foundations of the theory of differentiable manifolds and differentiable mappings: Cr-manifolds. Cr-mappings. Tangent space to a r-manifold. Cr-submanifolds. Cr-manifolds in RN. Immersion and submersion theorems. Regular and critical values of mappings. Topology on the space of r-mappings. Jets. Transversality. Stratification of algebraic and semi-algebraic manifolds. Transversality to stratification. Vector fields and dynamic systems: Vector fields on differentiable manifolds. Limit properties of dynamical systems. Examples of vector fields. Generic properties of parameter-dependent matrices. Linear dynamical systems and some notions from the theory of nonlinear dynamical systems. Grobman-Hartman theorem. Normal forms of differential equations. Poincare mapping. Invariant manifolds: Stable and unstable manifolds. Center manifolds. Generic bifurcations of vector fields and diffeomorphisms: Ljapunov-Schmidt method. Generic bifurcations of 1-parameter systems of vector fields in neighbourhoods of singular points. Generic bifurcations of 1-parameter systems of diffeomorphisms. Generic bifurcations of 1-parameter systems of vector fields in neighbourhoods of periodic trajectories. Complementary notes on the contemporary theory of dynamical systems: Generic bifurcations of multi-parameter systems of vector fields. Global theory of dynamical systems. Silnikov bifurcation. Global Hopf bifurcation. Attractors and chaotic sets.