Item type | Current location | Collection | Call number | Copy number | Status | Date due | Barcode |
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E-Books | Biblioteca da FCTUNL Online | Não Ficção | QA641.SPR FCT 98448 (Browse shelf) | 1 | Available |
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QA641.SPR FCT 98204 The geometry of spherically symmetric finsler manifolds | QA641.SPR FCT 98378 Information geometry and its applications | QA641.SPR FCT 98393 Kähler immersions of Kähler Manifolds into complex space forms | QA641.SPR FCT 98448 The restricted three-body problem and holomorphic curves | QA649.SPR FCT Developments in lorentzian geometry | QA649.SPR FCT 80805 Semiparallel submanifolds in space forms | QA649.SPR FCT 81022 Riemannian geometry of contact and symplectic manifolds |
Colocação: Online
The book serves as an introduction to holomorphic curves in symplectic manifolds, focusing on the case of four-dimensional symplectizations and symplectic cobordisms, and their applications to celestial mechanics. The authors study the restricted three-body problem using recent techniques coming from the theory of pseudo-holomorphic curves. The book starts with an introduction to relevant topics in symplectic topology and Hamiltonian dynamics before introducing some well-known systems from celestial mechanics, such as the Kepler problem and the restricted three-body problem. After an overview of different regularizations of these systems, the book continues with a discussion of periodic orbits and global surfaces of section for these and more general systems. The second half of the book is primarily dedicated to developing the theory of holomorphic curves - specifically the theory of fast finite energy planes - to elucidate the proofs of the existence results for global surfaces of section stated earlier. The book closes with a chapter summarizing the results of some numerical experiments related to finding periodic orbits and global surfaces of sections in the restricted three-body problem.
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