Hausdorff and packing dimensions for ergodic invariant measures of two-dimensional Lorenz transformations

Franz Hofbauer

Commentationes Mathematicae Universitatis Carolinae (2009)

  • Volume: 50, Issue: 2, page 221-243
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Hofbauer, Franz. "Hausdorff and packing dimensions for ergodic invariant measures of two-dimensional Lorenz transformations." Commentationes Mathematicae Universitatis Carolinae 50.2 (2009): 221-243. <http://eudml.org/doc/32495>.

@article{Hofbauer2009,
abstract = {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.},
author = {Hofbauer, Franz},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Hausdorff dimension; packing dimension; Lorenz transformation; ergodic measure; Hausdorff dimension; packing dimension; Lorenz transformation; ergodic measure},
language = {eng},
number = {2},
pages = {221-243},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Hausdorff and packing dimensions for ergodic invariant measures of two-dimensional Lorenz transformations},
url = {http://eudml.org/doc/32495},
volume = {50},
year = {2009},
}

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
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 2
SP - 221
EP - 243
AB - 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.
LA - eng
KW - Hausdorff dimension; packing dimension; Lorenz transformation; ergodic measure; Hausdorff dimension; packing dimension; Lorenz transformation; ergodic measure
UR - http://eudml.org/doc/32495
ER -

References

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