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Geometrical Themes Inspired by the N-body Problem [[electronic resource] /] / edited by Luis Hernández-Lamoneda, Haydeé Herrera, Rafael Herrera
| Geometrical Themes Inspired by the N-body Problem [[electronic resource] /] / edited by Luis Hernández-Lamoneda, Haydeé Herrera, Rafael Herrera |
| Edizione | [1st ed. 2018.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 |
| Descrizione fisica | 1 online resource (VII, 128 p. 26 illus., 7 illus. in color.) |
| Disciplina | 530.144 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Dynamics
Ergodic theory Calculus of variations Differential equations Geometry Manifolds (Mathematics) Complex manifolds Dynamical Systems and Ergodic Theory Calculus of Variations and Optimal Control; Optimization Ordinary Differential Equations Manifolds and Cell Complexes (incl. Diff.Topology) |
| ISBN | 3-319-71428-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Complex Differential Equations and Geometric Structures on Curves -- 1 Calogero's ``Goldfish,'' Complex Differential Equations and Translation Structures -- 1.1 The ``Goldfish'' Many-Body Problem -- 1.2 Differential Equations and Vector Fields -- 1.3 Translation Structures -- 1.4 Completeness and Semicompleteness -- 1.5 A Reduction -- 1.6 Translation Surfaces and Billiards -- 2 Affine Geometry -- 2.1 An Adapted Differential Operator -- 2.2 Uniformization of Triangles According to Schwarz, I -- 2.3 The Monodromy of the Linear Equation -- 2.4 Back to the Translation Surface -- 2.5 The Remaining Settings -- 3 Aside: Some Elliptic Functions -- 4 Projective Geometry -- 4.1 Möbius Transformations -- 4.2 The Equations of Chazy, Halphen and Ramanujan -- 4.3 Halphen's Invariance Property -- 4.4 The Schwarzian Derivative -- 4.5 Fuchs's Theorem -- 4.6 Schwarz and the Uniformization of Triangles, II -- 4.7 Extending Schwarz's Function -- 4.7.1 If α+β+γ1 (Spherical) -- 4.8 The Holonomy Cover -- 4.9 A Replacement for Translation Surfaces -- 4.10 Back to the Equations -- 4.11 Equations with Solutions Defined in More Unusual Domains -- 4.12 A General Construction -- 5 Epilogue -- References -- Blow-Up, Homotopy and Existence for Periodic Solutionsof the Planar Three-Body Problem -- 1 Introduction -- 1.1 My Path Through the Variational Wilderness -- 1.2 Breakthrough -- 2 Background: Equations and Solutions -- 2.1 Equations -- 2.2 Solutions of Euler and Lagrange -- 3 Shape Sphere: Blow-Up and Reduction, First Pass -- 4 Metric Set-Up: McGehee Blow-Up -- 4.1 Metric Reformulation -- 4.2 McGehee Transformation via Energy Balance -- 4.3 Equilibria! -- 4.3.1 The Euler and Lagrange Family: Planar Problems -- 4.3.2 Aside: An Open Problem -- 4.4 Linear and Angular Momentum.
4.5 Center of Mass Frame -- 4.6 Energy-Momentum Level Sets and the Standard Collision Manifold -- 4.7 Aside: Parabolic Infinity -- 5 Quotient by Rotations -- 5.1 Collision Locus -- 5.2 Accounting for Velocities -- 5.2.1 Velocity (Saari) Decomposition -- 5.2.2 Proof of Proposition 2 -- 5.3 Euler-Lagrange Family in Reduced Coordinates -- 6 A Gradient-Like Flow! -- 6.1 Making Moeckel's Manifold with Corner into a Manifold with a T -- 6.2 Finishing Up the Proof of Theorem 1 -- 7 A Conjecture: Non-existence -- 7.1 Hyperbolic Pants -- 7.2 Hanging Out at Infinity -- 7.3 The Bestiary of Danya Rose -- 7.3.1 Coding Gravitational Billiards -- 7.3.2 B-Mode, Unstable: t0 (8, 5) -- 7.3.3 Regularized Shape Sphere and Numerics -- 7.4 Failure of Limits -- References -- A Quick View of Lagrangian Floer Homology -- 1 Introduction -- 2 Morse-Smale Functions -- 3 Morse Homology -- 4 Symplectic Manifolds and Lagrangian Submanifolds -- 5 Symplectic and Hamiltonian Diffeomorphisms -- 6 Lagrangian Floer Homology -- 7 Computation of HF(L,L) -- 8 Applications -- References. |
| Record Nr. | UNISA-996466536703316 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Geometrical Themes Inspired by the N-body Problem / / edited by Luis Hernández-Lamoneda, Haydeé Herrera, Rafael Herrera
| Geometrical Themes Inspired by the N-body Problem / / edited by Luis Hernández-Lamoneda, Haydeé Herrera, Rafael Herrera |
| Edizione | [1st ed. 2018.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 |
| Descrizione fisica | 1 online resource (VII, 128 p. 26 illus., 7 illus. in color.) |
| Disciplina | 530.144 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Dynamics
Ergodic theory Calculus of variations Differential equations Geometry Manifolds (Mathematics) Complex manifolds Dynamical Systems and Ergodic Theory Calculus of Variations and Optimal Control; Optimization Ordinary Differential Equations Manifolds and Cell Complexes (incl. Diff.Topology) |
| ISBN | 3-319-71428-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Complex Differential Equations and Geometric Structures on Curves -- 1 Calogero's ``Goldfish,'' Complex Differential Equations and Translation Structures -- 1.1 The ``Goldfish'' Many-Body Problem -- 1.2 Differential Equations and Vector Fields -- 1.3 Translation Structures -- 1.4 Completeness and Semicompleteness -- 1.5 A Reduction -- 1.6 Translation Surfaces and Billiards -- 2 Affine Geometry -- 2.1 An Adapted Differential Operator -- 2.2 Uniformization of Triangles According to Schwarz, I -- 2.3 The Monodromy of the Linear Equation -- 2.4 Back to the Translation Surface -- 2.5 The Remaining Settings -- 3 Aside: Some Elliptic Functions -- 4 Projective Geometry -- 4.1 Möbius Transformations -- 4.2 The Equations of Chazy, Halphen and Ramanujan -- 4.3 Halphen's Invariance Property -- 4.4 The Schwarzian Derivative -- 4.5 Fuchs's Theorem -- 4.6 Schwarz and the Uniformization of Triangles, II -- 4.7 Extending Schwarz's Function -- 4.7.1 If α+β+γ1 (Spherical) -- 4.8 The Holonomy Cover -- 4.9 A Replacement for Translation Surfaces -- 4.10 Back to the Equations -- 4.11 Equations with Solutions Defined in More Unusual Domains -- 4.12 A General Construction -- 5 Epilogue -- References -- Blow-Up, Homotopy and Existence for Periodic Solutionsof the Planar Three-Body Problem -- 1 Introduction -- 1.1 My Path Through the Variational Wilderness -- 1.2 Breakthrough -- 2 Background: Equations and Solutions -- 2.1 Equations -- 2.2 Solutions of Euler and Lagrange -- 3 Shape Sphere: Blow-Up and Reduction, First Pass -- 4 Metric Set-Up: McGehee Blow-Up -- 4.1 Metric Reformulation -- 4.2 McGehee Transformation via Energy Balance -- 4.3 Equilibria! -- 4.3.1 The Euler and Lagrange Family: Planar Problems -- 4.3.2 Aside: An Open Problem -- 4.4 Linear and Angular Momentum.
4.5 Center of Mass Frame -- 4.6 Energy-Momentum Level Sets and the Standard Collision Manifold -- 4.7 Aside: Parabolic Infinity -- 5 Quotient by Rotations -- 5.1 Collision Locus -- 5.2 Accounting for Velocities -- 5.2.1 Velocity (Saari) Decomposition -- 5.2.2 Proof of Proposition 2 -- 5.3 Euler-Lagrange Family in Reduced Coordinates -- 6 A Gradient-Like Flow! -- 6.1 Making Moeckel's Manifold with Corner into a Manifold with a T -- 6.2 Finishing Up the Proof of Theorem 1 -- 7 A Conjecture: Non-existence -- 7.1 Hyperbolic Pants -- 7.2 Hanging Out at Infinity -- 7.3 The Bestiary of Danya Rose -- 7.3.1 Coding Gravitational Billiards -- 7.3.2 B-Mode, Unstable: t0 (8, 5) -- 7.3.3 Regularized Shape Sphere and Numerics -- 7.4 Failure of Limits -- References -- A Quick View of Lagrangian Floer Homology -- 1 Introduction -- 2 Morse-Smale Functions -- 3 Morse Homology -- 4 Symplectic Manifolds and Lagrangian Submanifolds -- 5 Symplectic and Hamiltonian Diffeomorphisms -- 6 Lagrangian Floer Homology -- 7 Computation of HF(L,L) -- 8 Applications -- References. |
| Record Nr. | UNINA-9910300122303321 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||