130465
20190416220452.0
doi
10.1017/S0143385708000874
0143-3857
ISI
000270772000006
ARTICLE
A Point is Normal for Almost All Maps beta x+ alpha mod 1 or Generalised beta-Transformations
2009
Cambridge University Press
2009
Journal Articles
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.
Piecewise Monotonic Transformations
Topological-Entropy
Turning-Point
Sets
(EPFLAUTH)128930
Faller, Bastien
128930
243461
Pfister, Charles-Edouard
106090
29
1529-1547
Ergodic Theory and Dynamical Systems
292942
http://infoscience.epfl.ch/record/130465/files/ETDS-Selfnormality-final_23_09_08.pdf
n/a
n/a
252205
GR-PF
U10947
oai:infoscience.tind.io:130465
SB
article
GLOBAL_SET
106090
GR-PF-ARTICLE-2008-008
EPFL
REVIEWED
PUBLISHED
ARTICLE