Geometrical Methods in the Theory of Ordinary Differential Equations - Taschenbuch

EAN (ISBN-13): 9781461269946
ISBN (ISBN-10): 1461269946
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 2012
Herausgeber: Springer New York Core >1 >T

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ISBN/EAN: 9781461269946

ISBN - alternative Schreibweisen:
1-4612-6994-6, 978-1-4612-6994-6
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: arnold, levi, feigenbaum, neistadt
Titel des Buches: geometrical methods ordinary equations, grundlehren mathematischen wissenschaften, something out the ordinary, geometrica, mathematisch, theory ordinary differential equations

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Daten vom Verlag:

Autor/in: V.I. Arnold
Titel: Grundlehren der mathematischen Wissenschaften; Geometrical Methods in the Theory of Ordinary Differential Equations
Verlag: Springer; Springer US
351 Seiten
Erscheinungsjahr: 2012-09-30
New York; NY; US
Gedruckt / Hergestellt in Niederlande.
Übersetzer/in: J. Szücs
Sprache: Englisch
213,99 € (DE)
219,99 € (AT)
236,00 CHF (CH)
POD
XIII, 351 p.

BC; Hardcover, Softcover / Mathematik/Analysis; Mathematische Analysis, allgemein; Verstehen; Mathematica; bifurcation; differential equation; hamiltonian system; ordinary differential equation; partial differential equation; schrödinger equation; stability; Analysis; Mathematics in Art and Architecture; Architectural History and Theory; Angewandte Mathematik; Architekturtheorie; Geschichte der Architektur; BB

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.