LEADER 04053nam 22007214a 450 001 9910827170003321 005 20200520144314.0 010 $a1-107-12735-1 010 $a1-280-41870-2 010 $a9786610418701 010 $a0-511-17762-3 010 $a0-511-03983-2 010 $a0-511-14803-8 010 $a0-511-30513-3 010 $a0-511-54318-2 010 $a0-511-05400-9 035 $a(CKB)1000000000008150 035 $a(EBL)201832 035 $a(OCoLC)437063287 035 $a(SSID)ssj0000263326 035 $a(PQKBManifestationID)11216117 035 $a(PQKBTitleCode)TC0000263326 035 $a(PQKBWorkID)10273075 035 $a(PQKB)10475006 035 $a(UkCbUP)CR9780511543180 035 $a(Au-PeEL)EBL201832 035 $a(CaPaEBR)ebr10023540 035 $a(CaONFJC)MIL41870 035 $a(MiAaPQ)EBC201832 035 $a(PPN)261308130 035 $a(EXLCZ)991000000000008150 100 $a20000426d2000 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTypical dynamics of volume preserving homeomorphisms /$fSteve Alpern, V.S. Prasad 205 $a1st ed. 210 $aCambridge ;$aNew York $cCambridge University Press$d2000 215 $a1 online resource (xix, 216 pages) $cdigital, PDF file(s) 225 1 $aCambridge tracts in mathematics ;$v139 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a0-521-17243-8 311 $a0-521-58287-3 320 $aIncludes bibliographical references (p. 205-211) and index. 327 $tVolume preserving homeomorphisms of the cube --$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]. 330 $aThis 2000 book provides a self-contained introduction to typical properties of homeomorphisms. Examples of properties of homeomorphisms considered include transitivity, chaos and ergodicity. A key idea here is the interrelation between typical properties of volume preserving homeomorphisms and typical properties of volume preserving bijections of the underlying measure space. The authors make the first part of this book very concrete by considering volume preserving homeomorphisms of the unit n-dimensional cube, and they go on to prove fixed point theorems (Conley-Zehnder- Franks). This is done in a number of short self-contained chapters which would be suitable for an undergraduate analysis seminar or a graduate lecture course. Much of this work describes the work of the two authors, over the last twenty years, in extending to different settings and properties, the celebrated result of Oxtoby and Ulam that for volume homeomorphisms of the unit cube, ergodicity is a typical property. 410 0$aCambridge tracts in mathematics ;$v139. 606 $aHomeomorphisms 606 $aMeasure-preserving transformations 615 0$aHomeomorphisms. 615 0$aMeasure-preserving transformations. 676 $a514 700 $aAlpern$b Steve$f1948-$0145016 701 $aPrasad$b V. S.$f1950-$065974 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910827170003321 996 $aTypical dynamics of volume preserving homeomorphisms$9378209 997 $aUNINA