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Mechanics, analysis and geometry : 200 years after Lagrange /
Providing a logically balanced and authoritative account of the different branches and problems of mathematical physics that Lagrange studied and developed, this volume presents up-to-date developments in differential goemetry, dynamical systems, the calculus of variations, and celestial and analyti...
| Clasificación: | Libro Electrónico |
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| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam ; New York : New York, N.Y., U.S.A. :
North-Holland ; Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.,
1991.
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| Colección: | North-Holland delta series.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Mechanics, Analysis and Geometry: 200 Years after Lagrange; Copyright Page; Foreword; Table of Contents; Part I: DYNAMICAL SYSTEMS; Chapter 1. Periodic Solutions near the Lagrange Equilibrium Points in the Restricted Three-Body Problem, for Mass Ratios near; 1. Introduction; 2. A lemma on commuting vector fields; 3. Application to hamiltonian systems; 4. Application to the restricted three-body problem; References; Chapter 2. Lower Bound on the Dimension of the Attractor for the Navier-Stokes Equations in Space Dimension 3; 1. Introduction; 2. The two dimensional case.
- 3. The three dimensional case4. Comparisons between u p per bounds and lower bounds; 5. Some inequalities (Appendix 1); 6. Upperbound of the dimension of the attractor in the 2D case (Appendix 2); 7. On the Orr-Sommerfeld equation (Appendix 3); References; Chapter 3. Homoclinic Chaos for Ray Optics in a Fiber: 200 Years after Lagrange; 1. Introduction; 2. Axisymmetric, Translation-Invariant Media; 3. Effects of Perturbations of The Refractive Index; Acknowledgements; References; Chapter 4. On the Vortex-Wave System; 1. Introduction; 2. Existence; 3. Many Vortices.
- 4. Uniqueness, Regularity and Final RemarksReferences; Part II: INTEGRABLE SYSTEMS AND QUANTUM GROUPS; Chapter 5. The Averaging Procedure for the Soliton-Like Solutions of Integrable Systems; 1. The general scheme; 2. The multiphase solutions of Benjamin-Ono equation; 3. Whithem equations; 4. The TLW equation; References; Chapter 6. A New Topological Invariant of Topological Hamiltonian Systems of Differential Equations and Applications to Probl; Definition; Statement 1; Statement 2; Theorem 1; Corollary; Statement 3; Theorem 2; Theorem 3; Statement 4; Proposition; Theorem 4; Theorem 5; Corollary.
- RemarkTheorem 6; Definition; Corollary; Theorem 7; Statement 5; Remark; Theorem 8; Definition; Theorem 9; Statement 6; References; Chapter 7. On the Lie Algebra of Motion Integrals for Two-Dimensional Hydrodynamic Equations in Clebsh Variables; 1 Two-dimensional in compressible hydrodynamics; 2 Clebsh variables and geometric integrals; 3 On the algebra of geometrical integrals; 4 The compressible hydrodynamics; 5 The integrable example; 6 The generalconstruction; References; Chapter 8. Quasiclassical Limit of Quantum Matrix Groups; 1. Introduction; 2. The Jacobi Identities.
- 3. Determinant Belongs to the Poisson Centre4. Comultiplication is a Poisson Map; Acknowledgement; References; Part III: ANALYTICAL MECHANICS AND CALCULUS OF VARIATIONS; Chapter 9. A Multisymplectic Framework for Classical Field Theory and the Calculus of Variations: I. Covariant Hamiltonian For; 1. Introduction; 2 Background; 3 Cartan Forms and Lepagean Equivalents; 4 Covariant Hamiltonian Formalism; 5 Regularity; 6 Special Cases; 7 Prospects; Acknowledgements; Appendix; References.