TY - EJOUR
DO - 10.1017/S0143385708000874
AB - We 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.
T1 - A Point is Normal for Almost All Maps beta x+ alpha mod 1 or Generalised beta-Transformations
DA - 2009
AU - Faller, Bastien
AU - Pfister, Charles-Edouard
JF - Ergodic Theory and Dynamical Systems
SP - 1529-1547
VL - 29
EP - 1529-1547
PB - Cambridge University Press
ID - 130465
KW - Piecewise Monotonic Transformations
KW - Topological-Entropy
KW - Turning-Point
KW - Sets
SN - 0143-3857
UR - http://infoscience.epfl.ch/record/130465/files/ETDS-Selfnormality-final_23_09_08.pdf
ER -