Geodesic
Weakly mixing rank-one transformations conjugate to their squares
Alexandre I. Danilenko1
1Max Planck Institute for Mathematics Vivatsgasse 7 Bonn, 53111, Germany and Institute for Low Temperature Physics & Engineering of Ukrainian National Academy of Sciences 47 Lenin Ave. Kharkov, 61164, Ukraine
Studia Mathematica, Tome 187 (2008) no. 1, pp. 75-93

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Utilizing the cut-and-stack techniques we construct explicitly a weakly mixing rigid rank-one transformation $T$ which is conjugate to $T^2$. Moreover, it is proved that for each odd $q$, there is such a $T$ commuting with a transformation of order $q$. For any $n$, we show the existence of a weakly mixing $T$ conjugate to $T^2$ and whose rank is finite and greater than $n$.
DOI : 10.4064/sm187-1-4
Keywords: utilizing cut and stack techniques construct explicitly weakly mixing rigid rank one transformation which conjugate moreover proved each odd there commuting transformation order existence weakly mixing conjugate whose rank finite greater

Alexandre I. Danilenko  1

1 Max Planck Institute for Mathematics Vivatsgasse 7 Bonn, 53111, Germany and Institute for Low Temperature Physics & Engineering of Ukrainian National Academy of Sciences 47 Lenin Ave. Kharkov, 61164, Ukraine 
Alexandre I. Danilenko. Weakly mixing rank-one transformations
 conjugate to their squares. Studia Mathematica, Tome 187 (2008) no. 1, pp. 75-93. doi: 10.4064/sm187-1-4
@article{10_4064_sm187_1_4,
     author = {Alexandre I. Danilenko},
     title = {Weakly mixing rank-one transformations
 conjugate to their squares},
     journal = {Studia Mathematica},
     pages = {75--93},
     year = {2008},
     volume = {187},
     number = {1},
     doi = {10.4064/sm187-1-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm187-1-4/}
}
TY  - JOUR
AU  - Alexandre I. Danilenko
TI  - Weakly mixing rank-one transformations
 conjugate to their squares
JO  - Studia Mathematica
PY  - 2008
SP  - 75
EP  - 93
VL  - 187
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm187-1-4/
DO  - 10.4064/sm187-1-4
LA  - en
ID  - 10_4064_sm187_1_4
ER  - 
%0 Journal Article
%A Alexandre I. Danilenko
%T Weakly mixing rank-one transformations
 conjugate to their squares
%J Studia Mathematica
%D 2008
%P 75-93
%V 187
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/sm187-1-4/
%R 10.4064/sm187-1-4
%G en
%F 10_4064_sm187_1_4

Cité par Sources :