000			03168nam a22003858i 4500
001			CR9780511543180
003			UkCbUP
005			20200124160239.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090505s2000||||enk o ||1 0|eng|d
020			_a9780511543180 (ebook)
020			_z9780521582872 (hardback)
020			_z9780521172431 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA613.7 _b.A46 2000
082	0	0	_a514 _221
100	1		_aAlpern, Steve, _d1948- _eauthor.
245	1	0	_aTypical dynamics of volume preserving homeomorphisms / _cSteve Alpern, V.S. Prasad.
264		1	_aCambridge : _bCambridge University Press, _c2000.
300			_a1 online resource (xix, 216 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge tracts in mathematics ; _v139
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0	0	_tVolume preserving homeomorphisms of the cube -- _tIntroduction to part I and II (compact manifolds) -- _tMeasure preserving homeomorphisms -- _tDiscrete approximations -- _tTransitive homeomorphisms of In and Rn -- _tFixed points and area preservation -- _tMeasure preserving lusin theorem -- _tErgodic homeomorphisms -- _tUniform approximation in g[In, delta] and generic properties in M[In, delta] -- _tMeasure preserving homeomorphisms of a compact manifold -- _tMeasures on compact manifolds -- _tDynamics on compact manifolds -- _tOeasure preserving homeomorphisms of a noncompact manifold -- _tErgodic volume preserving homeomorphisms of Rn -- _tManifolds where ergodicity is not generic -- _tNoncompact manifolds and ends -- _tErgodic homeomorphisms: the results -- _tErgodic homeomorphisms: proofs -- _tOther properties typical in M[X, u].
520			_aThis 2000 book provides a self-contained introduction to typical properties of homeomorphisms. Examples of properties of homeomorphisms considered include transitivity, chaos and ergodicity. A key idea here is the interrelation between typical properties of volume preserving homeomorphisms and typical properties of volume preserving bijections of the underlying measure space. The authors make the first part of this book very concrete by considering volume preserving homeomorphisms of the unit n-dimensional cube, and they go on to prove fixed point theorems (Conley-Zehnder- Franks). This is done in a number of short self-contained chapters which would be suitable for an undergraduate analysis seminar or a graduate lecture course. Much of this work describes the work of the two authors, over the last twenty years, in extending to different settings and properties, the celebrated result of Oxtoby and Ulam that for volume homeomorphisms of the unit cube, ergodicity is a typical property.
650		0	_aHomeomorphisms.
650		0	_aMeasure-preserving transformations.
700	1		_aPrasad, V. S., _d1950- _eauthor.
776	0	8	_iPrint version: _z9780521582872
830		0	_aCambridge tracts in mathematics ; _v139.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511543180
999			_c518321 _d518319