000			03614nam a22004813i 4500
001			EBC3114426
003			MiAaPQ
005			20240729124607.0
006			m o d |
007			cr cnu||||||||
008			240724s2003 xx o ||||0 eng d
020			_a9781470403737 _q(electronic bk.)
020			_z9780821832684
035			_a(MiAaPQ)EBC3114426
035			_a(Au-PeEL)EBL3114426
035			_a(CaPaEBR)ebr11041204
035			_a(OCoLC)922965090
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA614.83 -- .L63 2003eb
082	0		_a510 s;514/.74
100	1		_aLochak, P.
245	1	0	_aOn the Splitting of Invariant Manifolds in Multidimensional Near-Integrable Hamiltonian Systems.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2003.
264		4	_c©2003.
300			_a1 online resource (162 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.163
505	0		_aIntro -- Contents -- Chapter 0. Introduction and Some Salient Features of the Model Hamiltonian -- Chapter 1. Symplectic Geometry and the Splitting of Invariant Manifolds -- 1.1. Symplectic geometry: a short reminder -- 1.2. Hyperbolic invariant manifolds -- 1.3. Angles of Lagrangian planes: the symplectic viewpoint -- 1.4. Angles of Lagrangian planes: the Euclidean viewpoint -- 1.5. Symplectic isomorphisms, angles and splitting forms -- 1.6. The splitting of Lagrangian submanifolds -- 1.7. Lagrangian submanifolds in a cotangent bundle -- 1.8. Hyperbolic tori and normally hyperbolic invariant manifolds -- 1.9. The perturbative setting -- 1.10. Lagrangian intersections and homoclinic trajectories -- 1.11. The splitting of the invariant manifolds of hyperbolic tori -- Chapter 2. Estimating the Splitting Matrix Using Normal Forms -- 2.1. Resonant normal forms -- 2.2. Computations in the vicinity of a resonant surface -- 2.3. Splitting in a perturbative setting, variance and stability -- 2.4. General exponential estimates for the splitting matrix -- 2.5. Persistence of tori, invariant manifolds and homoclinic trajectories -- 2.6. Splitting and stability -- Chapter 3. The Hamilton-Jacobi Method for a Simple Resonance -- 3.1. Notation and assumptions -- 3.2. Formal solutions and the Hamilton-Jacobi algorithm -- 3.3. Convergence and domains of analyticity -- 3.4. Exponential closeness of the invariant manifolds -- 3.5. Linear versus nonlinear splitting -- 3.6. Some variants and possible generalizations -- 3.7. A short historical tour and some concluding remarks -- Appendix. Invariant Tori With Vanishing or Zero Torsion -- Bibliography.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aHamiltonian systems.
650		0	_aInvariant manifolds.
655		4	_aElectronic books.
700	1		_aMarco, J.-P.
700	1		_aSauzin, D.
776	0	8	_iPrint version: _aLochak, P. _tOn the Splitting of Invariant Manifolds in Multidimensional Near-Integrable Hamiltonian Systems _dProvidence : American Mathematical Society,c2003 _z9780821832684
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114426 _zClick to View
999			_c69921 _d69921