000			03748nam a22004813i 4500
001			EBC3113629
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005			20240729124547.0
006			m o d |
007			cr cnu||||||||
008			240724s1982 xx o ||||0 eng d
020			_a9781470406820 _q(electronic bk.)
020			_z9780821822722
035			_a(MiAaPQ)EBC3113629
035			_a(Au-PeEL)EBL3113629
035			_a(CaPaEBR)ebr10882288
035			_a(OCoLC)922981209
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA614.8 -- .R56 1983eb
082	0		_a510 s;514/.74
100	1		_aRimmer, Russell J.
245	1	0	_aGeneric Bifurications for Involutary Area Preserving Maps.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c1982.
264		4	_c©1983.
300			_a1 online resource (174 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.41
505	0		_aIntro -- TABLE OF CONTENTS -- CHAPTER 1. INTRODUCTION -- CHAPTER 2. PRELIMINARIES -- 2.1 Terminology and Some Useful Results -- 2.1.1 Basic Ideas -- 2.1.2 The Weak and the Strong Topologies -- 2.1.3 Transversality -- 2.2 A Curve of Fixed Points -- CHAPTER 3. BIFURCATION FROM A SYMMETRIC FIXED POINT WITH MULTIPLIERS ± 1 -- 3.1 A Generating Function for a Family of Area Preserving Maps -- 3.2 The Involutory Property and the Generating Functions -- 3.3 Fixed Points Near a Symmetric Fixed Point with Multipliers 1 -- 3.4 Periodic Points Near a Symmetric Fixed Point with Multipliers -1 -- CHAPTER 4. CONDITIONS ON GENERATING FUNCTIONS OCCUR GENERICALLY -- 4.1 A Dense, Open Set of Generating Functions -- 4.2 Preliminary Perturbations -- 4.3 D[sub(3)] and D[sub(4)] are Dense and Open -- 4.4 D[sub(1)] is Dense and Open -- CHAPTER 5. BIFURCATION FROM A SYMMETRIC FIXED POINT u[sub(o)] OF φ[sub(e)][sub(o)] WITH MULTIPLIERS WHICH ARE n[sup(th)] PRIME ROOTS OF UNITY, FOR n ≥ 3 -- 5.1 Periodic Points Bifurcating from (u[sub(o)], e[sub(o)]) -- CHAPTER 6. NORMALISATION OF A FAMILY OF INVOLUTORY AREA PRESERVING MAPS -- 6.1 The Linear Transformation -- 6.2 Normalisation of φ up to Terms of Order n 1 -- 6.3 Polar Coordinates -- CHAPTER 7. GENERIC BIFURCATIONS -- 7.1 The Generic Result -- 7.2 Proof of Lemma 7.1.2 when the Multipliers of φ[sub(e)][sub(o)] at u[sub(o) are 1 -- 7.3 Perturbation when the Multipliers of φ[sub(e)][sub(o)] at u[sub(o)]are n[sup(th)] prime Roots of Unity for n ≥ 2 eo ° 123 -- CHAPTER 8. FAMILIES OF INVOLUTORY AREA PRESERVING MAPS AND SYMMETRIC HAMILTONIAN SYSTEMS -- 8.1 Symmetric Hamiltonian Systems -- 8.2 Existence of Families of Involutory Area Preserving Maps -- APPENDIX 1 PROOFS OF TWO RESULTS USED IN CHAPTER 4 -- A1.1Proof of Proposition 4.2.2(ii) -- A1.2 Proof of Lemma 4.2.4 -- REFERENCES.
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	_aDifferentiable dynamical systems.
650		0	_aMappings (Mathematics).
650		0	_aBifurcation theory.
650		0	_aHamiltonian systems.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aRimmer, Russell J. _tGeneric Bifurications for Involutary Area Preserving Maps _dProvidence : American Mathematical Society,c1982 _z9780821822722
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3113629 _zClick to View
999			_c69162 _d69162