000			02159cam a22002774a 4500
001			14966565
005			20250612180617.0
008			070814s2008 riua b 001 0 eng
020			_a9780821887332
040			_aCSL _cCSL
041			_2eng _aeng
084			_aB325 P8 NBHM _qCSL
100	1		_aSilva, C. E. _eauthor. _9812757
245	1	0	_aInvitation to ergodic theory
260			_aProvidence : _bAmerican Mathematical Society, _c2008.
300			_aix, 262 p. : _bill. ; _c22 cm.
490	0		_aStudent mathematical library ; _v42
504			_aIncludes bibliographical references and index.
520			_aThis book is an introduction to basic concepts in ergodic theory such as recurrence, ergodicity, the ergodic theorem, mixing, and weak mixing. It does not assume knowledge of measure theory; all the results needed from measure theory are presented from scratch. In particular, the book includes a detailed construction of the Lebesgue measure on the real line and an introduction to measure spaces up to the Carathéodory extension theorem. It also develops the Lebesgue theory of integration, including the dominated convergence theorem and an introduction to the Lebesgue spaces. Several examples of a dynamical system are developed in detail to illustrate various dynamical concepts. These include in particular the baker's transformation, irrational rotations, the dyadic odometer, the Hajian–Kakutani transformation, the Gauss transformation, and the Chacón transformation. There is a detailed discussion of cutting and stacking transformations in ergodic theory. The book includes several exercises and some open questions to give the flavor of current research. The book also introduces some notions from topological dynamics, such as minimality, transitivity and symbolic spaces; and develops some metric topology, including the Baire category theorem.
650		0	_aErgodic theory.
650		0	_aLebesgue measure. _9812758
650		0	_aRecurrence and ergodicity. _9812759
650		0	_a Ergodic theorem _9812760
650		0	_aMixing notions _9812761
942			_2CC _n0 _cTEXL _hB325 P8 NBHM
999			_c1431675 _d1431675