Geodesic
Hausdorff and packing dimensions for ergodic invariant measures of two-dimensional Lorenz transformations
Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 2, pp. 221-243

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR   Zbl

We extend the notions of Hausdorff and packing dimension introducing weights in their definition. These dimensions are computed for ergodic invariant probability measures of two-dimensional Lorenz transformations, which are transformations of the type occuring as first return maps to a certain cross section for the Lorenz differential equation. We give a formula of the dimensions of such measures in terms of entropy and Lyapunov exponents. This is done for two choices of the weights using the recurrence time of a set and equilibrium states respectively.
We extend the notions of Hausdorff and packing dimension introducing weights in their definition. These dimensions are computed for ergodic invariant probability measures of two-dimensional Lorenz transformations, which are transformations of the type occuring as first return maps to a certain cross section for the Lorenz differential equation. We give a formula of the dimensions of such measures in terms of entropy and Lyapunov exponents. This is done for two choices of the weights using the recurrence time of a set and equilibrium states respectively.
Classification : 28A78, 37A35, 37C45, 37D50
Keywords: Hausdorff dimension; packing dimension; Lorenz transformation; ergodic measure 
Hofbauer, Franz. Hausdorff and packing dimensions for ergodic invariant measures of two-dimensional Lorenz transformations. Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 2, pp. 221-243. http://geodesic.mathdoc.fr/item/CMUC_2009_50_2_a4/
@article{CMUC_2009_50_2_a4,
     author = {Hofbauer, Franz},
     title = {Hausdorff and packing dimensions for ergodic invariant measures of two-dimensional {Lorenz} transformations},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {221--243},
     year = {2009},
     volume = {50},
     number = {2},
     mrnumber = {2537833},
     zbl = {1212.37064},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2009_50_2_a4/}
}
TY  - JOUR
AU  - Hofbauer, Franz
TI  - Hausdorff and packing dimensions for ergodic invariant measures of two-dimensional Lorenz transformations
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2009
SP  - 221
EP  - 243
VL  - 50
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMUC_2009_50_2_a4/
LA  - en
ID  - CMUC_2009_50_2_a4
ER  - 
%0 Journal Article
%A Hofbauer, Franz
%T Hausdorff and packing dimensions for ergodic invariant measures of two-dimensional Lorenz transformations
%J Commentationes Mathematicae Universitatis Carolinae
%D 2009
%P 221-243
%V 50
%N 2
%U http://geodesic.mathdoc.fr/item/CMUC_2009_50_2_a4/
%G en
%F CMUC_2009_50_2_a4