000			02486cam a22002654a 4500
001			13944822
005			20250611153233.0
008			050427s2005 flua b 001 0 eng
020			_a9780367413323
040			_aCSL _cCSL
041			_2eng _aeng
084			_aB6 : 3 P5 NBHM _qCSL
100	1		_aBurns, Keith, _eauthor. _9812637
245	1	0	_aDifferential geometry and topology : _bwith a view to dynamical systems
260			_aBoca Raton : _bCRC Press, _c2005.
300			_aix, 389 p. : _bill. ; _c24 cm.
440		0	_aStudies in advanced mathematics _9812638
504			_aIncludes bibliographical references (p. 379-383) and index.
520			_aAccessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow. Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential forms, and integration on manifolds provide the foundation for many applications in dynamical systems and mechanics. The authors also discuss the Gauss-Bonnet theorem and its implications in non-Euclidean geometry models. The differential topology aspect of the book centers on classical, transversality theory, Sard's theorem, intersection theory, and fixed-point theorems. The construction of the de Rham cohomology builds further arguments for the strong connection between the differential structure and the topological structure. It also furnishes some of the tools necessary for a complete understanding of the Morse theory. These discussions are followed by an introduction to the theory of hyperbolic systems, with emphasis on the quintessential role of the geodesic flow. The integration of geometric theory, topological theory, and concrete applications to dynamical systems set this book apart. With clean, clear prose and effective examples, the authors' intuitive approach creates a treatment that is comprehensible to relative beginners, yet rigorous enough for those with more background and experience in the field.
650		0	_aGeometry, Differential. _9812572
650		0	_aDifferential topology.
650		0	_aDifferentiable dynamical systems. _9717560
700	1		_aGidea, Marian. _eco-author. _9812639
942			_2CC _n0 _cTEXL _hB6 : 3 P5 NBHM
999			_c1431621 _d1431621