000			02730cam a2200253 a 4500
001			vtls000001665
003			VRT
005			20250102224223.0
008			081108s1989 enka |b 001 0 eng
020			_a0521236320 (pbk.)
020			_a0521389976 (hard)
039		9	_a201402040100 _bVLOAD _c201007191155 _dmalmash _c200811091230 _dvenkatrajand _c200811081251 _dNoora _y200811081247 _zNoora
050	0	0	_aQA313 _b.P47 1989
100	1		_aPetersen, Karl Endel, _d1943- _937815
245	1	0	_aErgodic Theory / _cKarl Petersen.
260			_aCambridge ; _aNew York : _bCambridge University Press, _c1989.
300			_axi, 329 p. : _bill. ; _c23 cm.
440		0	_aCambridge studies in advanced mathematics ; _v2 _937816
504			_aIncludes bibliographical referneces (p. [302]-321) and index.
505			_aPreface; 1. Introduction and preliminaries; 2. The fundamentals of ergodic theory; 3. More about almost everywhere convergence; 4. More about recurrence; 5. Entropy; 6. More about entropy; References; Index.
520			_aThe study of dynamical systems forms a vast and rapidly developing field even when one considers only activity whose methods derive mainly from measure theory and functional analysis. Karl Petersen has written a book which presents the fundamentals of the ergodic theory of point transformations and then several advanced topics which are currently undergoing intense research. By selecting one or more of these topics to focus on, the reader can quickly approach the specialized literature and indeed the frontier of the area of interest. Each of the four basic aspects of ergodic theory - examples, convergence theorems, recurrence properties, and entropy - receives first a basic and then a more advanced, particularized treatment. At the introductory level, the book provides clear and complete discussions of the standard examples, the mean and pointwise ergodic theorems, recurrence, ergodicity, weak mixing, strong mixing, and the fundamentals of entropy. Among the advanced topics are a thorough treatment of maximal functions and their usefulness in ergodic theory, analysis, and probability, an introduction to almost-periodic functions and topological dynamics, a proof of the Jewett-Krieger Theorem, an introduction to multiple recurrence and the Szemeredi-Furstenberg Theorem, and the Keane-Smorodinsky proof of Ornstein's Isomorphism Theorem for Bernoulli shifts. The author's easily-readable style combined with the profusion of exercises and references, summaries, historical remarks, and heuristic discussions make this book useful either as a text for graduate students or self-study, or as a reference work for the initiated.
650		0	_aErgodic theory. _937817
942			_2lcc _n0 _cBK
999			_c16804 _d16804