000130465 001__ 130465
000130465 005__ 20190416220452.0
000130465 0247_ $$2doi$$a10.1017/S0143385708000874
000130465 022__ $$a0143-3857
000130465 02470 $$2ISI$$a000270772000006
000130465 037__ $$aARTICLE
000130465 245__ $$aA Point is Normal for Almost All Maps beta x+ alpha mod 1 or Generalised beta-Transformations
000130465 269__ $$a2009
000130465 260__ $$bCambridge University Press$$c2009
000130465 336__ $$aJournal Articles
000130465 520__ $$aWe consider the map T-alpha,T-beta(x) := beta x + alpha mod 1, which admits a unique probability measure of maximal entropy. For x is an element of [0, 1], we show that the orbit of x is mu(alpha,beta)-normal for almost all (alpha, beta) is an element of [0, 1) x ( 1, infinity) (with respect to Lebesgue measure). Nevertheless, we construct analytic curves in [0, 1) x (1, infinity) along which the orbit of x = 0 is mu(alpha,beta)-normal at no more than one point. These curves are disjoint and fill the set [0, 1) x (1, infinity). We also study the generalized-transformations (in particular, the tent Map). We show that the critical orbit x = 1 is normal with respect to the measure of maximal entropy for almost all beta.
000130465 6531_ $$aPiecewise Monotonic Transformations
000130465 6531_ $$aTopological-Entropy
000130465 6531_ $$aTurning-Point
000130465 6531_ $$aSets
000130465 700__ $$0(EPFLAUTH)128930$$g128930$$aFaller, Bastien
000130465 700__ $$aPfister, Charles-Edouard$$g106090$$0243461
000130465 773__ $$j29$$tErgodic Theory and Dynamical Systems$$q1529-1547
000130465 8564_ $$uhttps://infoscience.epfl.ch/record/130465/files/ETDS-Selfnormality-final_23_09_08.pdf$$zn/a$$s292942$$yn/a
000130465 909C0 $$xU10947$$0252205$$pGR-PF
000130465 909CO $$ooai:infoscience.tind.io:130465$$qGLOBAL_SET$$pSB$$particle
000130465 917Z8 $$x106090
000130465 937__ $$aGR-PF-ARTICLE-2008-008
000130465 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000130465 980__ $$aARTICLE