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006			m |o d |
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008			180829s2018 gw |||| o |||| 0|eng
010			_a 2019736271
020			_a9783030101800 (Pbk)
024	7		_a10.1007/978-3-319-72278-8 _2doi
035			_a(DE-He213)978-3-319-72278-8
040			_aDLC _beng _epn _erda _cIISERB
072		7	_aMAT012030 _2bisacsh
072		7	_aPBMP _2bicssc
072		7	_aPBMP _2thema
082	0	4	_a516.36 F86R _223
100	1		_aFrauenfelder, Urs. _eauthor. _930453
245	1	4	_aRestricted Three-Body Problem and Holomorphic Curves _cby Urs Frauenfelder, Otto van Koert.
250			_a1st ed. 2018.
260			_aSwitzarland: _bSpringer-Nature, _c2018.
300			_aXI, 374 pages
490	1		_aPathways in Mathematics, _x2367-3451
505	0		_aIntroduction -- Symplectic geometry and Hamiltonian mechanics -- Symmetries -- Regularization of two body collisions -- The restricted three body problem -- Contact geometry and the restricted three body problem -- Periodic orbits in Hamiltonian systems -- Periodic orbits in the restricted three body problem -- Global surfaces of section -- The Maslov Index -- Spectral flow -- Convexity -- Finite energy planes -- Siefring's intersection theory for fast finite energy planes -- The moduli space of fast finite energy planes -- Compactness -- Construction of global surfaces of section -- Numerics and dynamics via global surfaces of section.
520			_aThe 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.
650		0	_aDifferential geometry. _930454
650		0	_aFunctions of complex variables. _930455
650	1	4	_aDifferential Geometry. _930456
650	2	4	_aSeveral Complex Variables and Analytic Spaces. _930457
700	1		_avan Koert, Otto. _eauthor. _930458
776	0	8	_iPrint version: _tThe restricted three-body problem and holomorphic curves _z9783319722771 _w(DLC) 2018953209
776	0	8	_iPrinted edition: _z9783030101800
776	0	8	_iPrinted edition: _z9783319722771
776	0	8	_iPrinted edition: _z9783319722795
830		0	_aPathways in Mathematics, _930459
906			_a0 _bibc _corigres _du _encip _f20 _gy-gencatlg
942			_2ddc _cBK
999			_c10331 _d10331