| Title:
|
Hausdorff and packing dimensions for ergodic invariant measures of two-dimensional Lorenz transformations (English) |
| Author:
|
Hofbauer, Franz |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
50 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
221-243 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Hausdorff dimension |
| Keyword:
|
packing dimension |
| Keyword:
|
Lorenz transformation |
| Keyword:
|
ergodic measure |
| MSC:
|
28A78 |
| MSC:
|
37A35 |
| MSC:
|
37C45 |
| MSC:
|
37D50 |
| idZBL:
|
Zbl 1212.37064 |
| idMR:
|
MR2537833 |
| . |
| Date available:
|
2009-08-18T12:24:47Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133430 |
| . |
| Reference:
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