000			04501nam a22004933i 4500
001			EBC4908543
003			MiAaPQ
005			20240729131329.0
006			m o d |
007			cr cnu||||||||
008			240724s2010 xx o ||||0 fre d
020			_a9781470418076 _q(electronic bk.)
020			_z9780821847183
035			_a(MiAaPQ)EBC4908543
035			_a(Au-PeEL)EBL4908543
035			_a(CaPaEBR)ebr11410084
035			_a(OCoLC)993758513
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQ143.P7.H475 2010
082	0		_a510
100	1		_aCharpentier, Éric.
245	1	4	_aThe Scientific Legacy of Poincaré.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2010.
264		4	_c©2010.
300			_a1 online resource (410 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aHistory of Mathematics ; _vv.36
505	0		_aCover -- Title page -- Contents -- List of authors -- Translator's note -- Introduction -- Poincaré and his disk -- Differential equations with algebraic coefficients over arithmetic manifolds -- Poincaré and analytic number theory -- The theory of limit cycles -- Singular points of differential equations: On a theorem of Poincaré -- Periodic orbits of the three body problem: Early history, contributions of Hill and Poincaré, and some recent developments -- On the existence of closed geodesics -- Poincaré's memoir for the Prize of King Oscar II: Celestial harmony entangled in homoclinic intersections -- Variations on Poincaré's recurrence theorem -- Low-dimensional chaos and asymptotic time behavior in the mechanics of fluids -- The concept of "residue" after Poincaré: Cutting across all of mathematics -- The proof of the Poincaré conjecture, according to Perelman -- Henri Poincaré and the partial differential equations of mathematical physics -- Poincaré's calculus of probabilities -- Poincaré and geometric probability -- Poincaré and Lie's third theorem -- The Poincaré group -- Henri Poincaré as an applied mathematician -- Henri Poincaré and his thoughts on the philosophy of science -- Back Cover.
520			_aHenri Poincaré (1854-1912) was one of the greatest scientists of his time, perhaps the last one to have mastered and expanded almost all areas in mathematics and theoretical physics. He created new mathematical branches, such as algebraic topology, dynamical systems, and automorphic functions, and he opened the way to complex analysis with several variables and to the modern approach to asymptotic expansions. He revolutionized celestial mechanics, discovering deterministic chaos. In physics, he is one of the fathers of special relativity, and his work in the philosophy of sciences is illuminating. For this book, about twenty world experts were asked to present one part of Poincaré's extraordinary work. Each chapter treats one theme, presenting Poincaré's approach, and achievements, along with examples of recent applications and some current prospects. Their contributions emphasize the power and modernity of the work of Poincaré, an inexhaustible source of inspiration for researchers, as illustrated by the Fields Medal awarded in 2006 to Grigori Perelman for his proof of the Poincaré conjecture stated a century before. This book can be read by anyone with a master's (even a bachelor's) degree in mathematics, or physics, or more generally by anyone who likes mathematical and physical ideas. Rather than presenting detailed proofs, the main ideas are explained, and a bibliography is provided for those who wish to understand the technical details.
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	_aChaotic behavior in systems.
655		4	_aElectronic books.
700	1		_aGhys, Étienne.
700	1		_aLesne, Annick.
700	1		_aBowman, Joshua.
776	0	8	_iPrint version: _aCharpentier, Éric _tThe Scientific Legacy of Poincaré _dProvidence : American Mathematical Society,c2010 _z9780821847183
797	2		_aProQuest (Firm)
830		0	_aHistory of Mathematics
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4908543 _zClick to View
999			_c128052 _d128052