000			03739nam a22003858i 4500
001			CR9780511758898
003			UkCbUP
005			20200124160236.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			100430s2000||||enk o ||1 0|eng|d
020			_a9780511758898 (ebook)
020			_z9780521660303 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA611.5 _b.B42 2000
082	0	4	_a515.42 _221
100	1		_aBekka, M. Bachir, _eauthor.
245	1	0	_aErgodic theory and topological dynamics of group actions on homogeneous spaces / _cM. Bachir Bekka, Matthias Mayer.
246	3		_aErgodic Theory & Topological Dynamics of Group Actions on Homogeneous Spaces
264		1	_aCambridge : _bCambridge University Press, _c2000.
300			_a1 online resource (x, 200 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aLondon Mathematical Society lecture note series ; _v269
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0	0	_tErgodic Systems -- _tExamples and Basic Results -- _tErgodic Theory and Unitary Representations -- _tInvariant Measures and Unique Ergodicity -- _tThe Geodesic Flow of Riemannian Locally Symmetric Spaces -- _tSome Hyperbolic Geometry -- _tLattices and Fundamental Domains -- _tThe Geodesic Flow of Compact Riemann Surfaces -- _tThe Geodesic Flow on Riemannian Locally Symmetric Spaces -- _tThe Vanishing Theorem of Howe and Moore -- _tHowe--Moore's Theorem -- _tMoore's Ergodicity Theorems -- _tCounting Lattice Points in the Hyperbolic Plane -- _tMixing of All Orders -- _tThe Horocycle Flow -- _tThe Horocycle Flow of a Riemann Surface -- _tProof of Hedlund's Theorem--Cocompact Case -- _tClassification of Invariant Measures -- _tEquidistribution of Horocycle Orbits -- _tSiegel Sets, Mahler's Criterion and Margulis' Lemma -- _tSiegel Sets in SL(n, R) -- _tSL(n, Z) is a lattice in SL(n, R) -- _tMahler's Criterion -- _tReduction of Positive Definite Quadratic Forms -- _tMargulis' Lemma -- _tAn Application to Number Theory: Oppenheim's Conjecture -- _tOppenheim's Conjecture -- _tProof of the Theorem--Preliminaries -- _tExistence of Minimal Closed Subsets -- _tOrbits of One-Parameter Groups of Unipotent Linear Transformations -- _tProof of the Theorem--Conclusion -- _tRatner's Results on the Conjectures of Raghunathan, Dani and Margulis.
520			_aThe study of geodesic flows on homogenous spaces is an area of research that has yielded some fascinating developments. This book, first published in 2000, focuses on many of these, and one of its highlights is an elementary and complete proof (due to Margulis and Dani) of Oppenheim's conjecture. Also included here: an exposition of Ratner's work on Raghunathan's conjectures; a complete proof of the Howe-Moore vanishing theorem for general semisimple Lie groups; a new treatment of Mautner's result on the geodesic flow of a Riemannian symmetric space; Mozes' result about mixing of all orders and the asymptotic distribution of lattice points in the hyperbolic plane; Ledrappier's example of a mixing action which is not a mixing of all orders. The treatment is as self-contained and elementary as possible. It should appeal to graduate students and researchers interested in dynamical systems, harmonic analysis, differential geometry, Lie theory and number theory.
650		0	_aErgodic theory.
650		0	_aTopological dynamics.
700	1		_aMayer, Matthias _c(Mathematician), _eauthor.
776	0	8	_iPrint version: _z9780521660303
830		0	_aLondon Mathematical Society lecture note series ; _v269.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511758898
999			_c518106 _d518104