Geometrical Methods in the Theory of Ordinary Differential Equations (2nd Edn) (Grundlehren Der Mathematischen Wissenschaften) (Volume 250)

Arnold, V.I. and Szucs, J (trans)

ISBN 10: 0387966498 / ISBN 13: 9780387966496

Editore: Springer, 1988

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Volume 250. This is an ex-library book and may have the usual library/used-book markings inside.This book has hardback covers. In fair condition, suitable as a study copy. No dust jacket. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,750grams, ISBN:9780387966496.

Codice articolo 9790586

Dati bibliografici

• Titolo: Geometrical Methods in the Theory of Ordinary Differential Equations (2nd Edn) (Grundlehren Der Mathematischen Wissenschaften) (Volume 250)
• Editore: Springer
• Data di pubblicazione: 1988
• Lingua: Inglese
• ISBN 10: 0387966498
• ISBN 13: 9780387966496
• Rilegatura: Rilegato
• Edizione: seconda edizione
• Condizione: Fair
• Peso: 750 grammi
• Cataloghi dei venditori:
  • Mathematics

Descrizione articolo

Riassunto

Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has been made partly with the help of computers.

Contenuti

1 Special Equations.- § 1. Differential Equations Invariant under Groups of Symmetries.- § 2. Resolution of Singularities of Differential Equations.- § 3. Implicit Equations.- § 4. Normal Form of an Implicit Differential Equation in the Neighborhood of a Regular Singular Point.- § 5. The Stationary Schrödinger Equation.- § 6. Geometry of a Second-Order Differential Equation and Geometry of a Pair of Direction Fields in Three-Dimensional Space.- 2 First-Order Partial Differential Equations.- § 7. Linear and Quasilinear First-Order Partial Differential Equations.- § 8. The Nonlinear First-Order Partial Differential Equation.- § 9. A Theorem of Frobenius.- 3 Structural Stability.- § 10. The Notion of Structural Stability.- §11. Differential Equations on the Torus.- § 12. Analytic Reduction of Analytic Circle Diffeomorphisms to a Rotation.- § 13. Introduction to the Hyperbolic Theory.- § 14. Anosov Systems.- § 15. Structurally Stable Systems Are Not Everywhere Dense.- 4 Perturbation Theory.- § 16. The Averaging Method.- § 17. Averaging in Single-Frequency Systems.- § 18. Averaging in Systems with Several Frequencies.- § 19. Averaging in Hamiltonian Systems.- § 20. Adiabatic Invariants.- § 21. Averaging in Seifert’s Foliation.- 5 Normal Forms.- § 22. Formal Reduction to Linear Normal Forms.- § 23. The Case of Resonance.- § 24. Poincaré and Siegel Domains.- § 25. Normal Form of a Mapping in the Neighborhood of a Fixed Point.- § 26. Normal Form of an Equation with Periodic Coefficients.- § 27. Normal Form of the Neighborhood of an Elliptic Curve.- § 28. Proof of Siegel’s Theorem.- 6 Local Bifurcation Theory.- § 29. Families and Deformations.- § 30. Matrices Depending on Parameters and Singularities of the Decrement Diagram.- §31. Bifurcations of Singular Points of a Vector Field.- § 32. Versal Deformations of Phase Portraits.- § 33. Loss of Stability of an Equilibrium Position.- § 34. Loss of Stability of Self-Sustained Oscillations.- § 35. Versal Deformations of Equivariant Vector Fields on the Plane.- § 36. Metamorphoses of the Topology at Resonances.- § 37. Classification of Singular Points.- Samples of Examination Problems.