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010   $a3-319-72278-6
024 7 $a10.1007/978-3-319-72278-8
035   $a(CKB)4100000006098327
035   $a(MiAaPQ)EBC5504892
035   $a(DE-He213)978-3-319-72278-8
035   $a(PPN)229917968
035   $a(EXLCZ)994100000006098327
100   $a20180829d2018      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 14$aThe Restricted Three-Body Problem and Holomorphic Curves /$fby Urs Frauenfelder, Otto van Koert
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2018.
215   $a1 online resource (381 pages)
225 1 $aPathways in Mathematics,$x2367-3451
311   $a3-319-72277-8 
327   $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.
330   $aThe book serves as an introduction to holomorphic curves in symplectic manifolds, focusing on the case of four-dimensional symplectizations and symplectic cobordisms, and their applications to celestial mechanics. The authors study the restricted three-body problem using recent techniques coming from the theory of pseudo-holomorphic curves. The book starts with an introduction to relevant topics in symplectic topology and Hamiltonian dynamics before introducing some well-known systems from celestial mechanics, such as the Kepler problem and the restricted three-body problem. After an overview of different regularizations of these systems, the book continues with a discussion of periodic orbits and global surfaces of section for these and more general systems. The second half of the book is primarily dedicated to developing the theory of holomorphic curves - specifically the theory of fast finite energy planes - to elucidate the proofs of the existence results for global surfaces of section stated earlier. The book closes with a chapter summarizing the results of some numerical experiments related to finding periodic orbits and global surfaces of sections in the restricted three-body problem.
410  0$aPathways in Mathematics,$x2367-3451
606   $aGeometry, Differential
606   $aFunctions of complex variables
606   $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022
606   $aSeveral Complex Variables and Analytic Spaces$3https://scigraph.springernature.com/ontologies/product-market-codes/M12198
615  0$aGeometry, Differential.
615  0$aFunctions of complex variables.
615 14$aDifferential Geometry.
615 24$aSeveral Complex Variables and Analytic Spaces.
676   $a515.98
700   $aFrauenfelder$b Urs$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767924
702   $avan Koert$b Otto$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910300136603321
996   $aThe Restricted Three-Body Problem and Holomorphic Curves$92124846
997   $aUNINA