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Convexity of Singular Affine Structures and Toric-Focus Integrable Hamiltonian Systems
| Convexity of Singular Affine Structures and Toric-Focus Integrable Hamiltonian Systems |
| Autore | Ratiu Tudor S |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Providence : , : American Mathematical Society, , 2023 |
| Descrizione fisica | 1 online resource (102 pages) |
| Disciplina |
516/.08
516.08 |
| Altri autori (Persone) |
WacheuxChristophe
ZungNguyen Tien |
| Collana | Memoirs of the American Mathematical Society Series |
| Soggetto topico |
Convex domains
Affine differential geometry Hamiltonian systems Toric varieties Dynamical systems and ergodic theory -- Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems -- Completely integrable systems, topological structure of phase space, integratio Differential geometry -- Classical differential geometry -- Affine differential geometry Convex and discrete geometry -- General convexity -- Axiomatic and generalized convexity |
| ISBN | 1-4704-7540-5 |
| Classificazione | 37J3553A1552A01 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title page -- Chapter 1. Introduction -- Positive convexity results -- Negative convexity results -- Organization of the paper -- Acknowledgment -- Chapter 2. A brief overview of convexity in symplectic geometry and in integrable Hamiltonian systems -- 2.1. Kostant's Linear Convexity Theorem -- 2.2. Infinite dimensional Lie theory -- 2.3. "Linear" symplectic formulations -- 2.4. "Non-linear" symplectic formulations -- 2.5. Local-Global Convexity Principle -- 2.6. Convexity in integrable Hamiltonian systems -- Chapter 3. Toric-focus integrable Hamiltonian systems -- 3.1. Integrable systems -- 3.2. Local normal form of non-degenerate singularities -- 3.3. Semi-local structure of singularities -- 3.4. Topology and differential structure of the base space -- 3.5. Integral affine structure on the base space -- Chapter 4. Base spaces and affine manifolds with focus singularities -- 4.1. Monodromy and affine coordinates near elementary focus points -- 4.2. Affine coordinates near focus points in higher dimensions -- 4.3. Behavior of the affine structure near focus^{ } points -- 4.4. Definition of affine structures with focus points -- Chapter 5. Straight lines and convexity -- 5.1. Regular and singular straight lines -- 5.2. Singular straight lines in dimension 2 and branched extension -- 5.3. Straight lines in dimension near a focus point -- 5.4. Straight lines near a focus^{ } point -- 5.5. The notions of convexity and strong convexity -- Chapter 6. Local convexity at focus points -- 6.1. Convexity of focus boxes in dimension 2 -- 6.2. Convexity of focus boxes in higher dimensions -- 6.3. Existence of non-convex focus^{ } boxes -- Chapter 7. Global convexity -- 7.1. Local-global convexity principle -- 7.2. Angle variation of a curve on an affine surface -- 7.3. Convexity of compact affine surfaces with non-empty boundary.
7.4. Convexity in the non-compact proper case -- 7.5. Non-convex examples in the non-proper case -- 7.6. An affine black hole and non-convex ² -- 7.7. A globally convex ² example -- 7.8. Convexity of toric-focus base spaces in higher dimensions -- Bibliography -- Index -- Back Cover. |
| Record Nr. | UNINA-9910915797003321 |
Ratiu Tudor S
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| Providence : , : American Mathematical Society, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Geometry and Dynamics of Integrable Systems / / by Alexey Bolsinov, Juan J. Morales-Ruiz, Nguyen Tien Zung ; edited by Eva Miranda, Vladimir Matveev
| Geometry and Dynamics of Integrable Systems / / by Alexey Bolsinov, Juan J. Morales-Ruiz, Nguyen Tien Zung ; edited by Eva Miranda, Vladimir Matveev |
| Autore | Bolsinov Alexey |
| Edizione | [1st ed. 2016.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2016 |
| Descrizione fisica | 1 online resource (VIII, 140 p. 22 illus., 3 illus. in color.) |
| Disciplina | 516.35 |
| Collana | Advanced Courses in Mathematics - CRM Barcelona |
| Soggetto topico |
Dynamics
Ergodic theory Geometry, Differential Algebra Field theory (Physics) Dynamical Systems and Ergodic Theory Differential Geometry Field Theory and Polynomials |
| ISBN | 3-319-33503-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Integrable Systems and Differential Galois Theory -- Singularities of bi-Hamiltonian Systems and Stability Analysis -- Geometry of Integrable non-Hamiltonian Systems. |
| Record Nr. | UNINA-9910254092103321 |
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Bolsinov Alexey
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| Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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