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
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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.
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 
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     author = {Hofbauer, Franz},
     title = {Hausdorff and packing dimensions for ergodic invariant measures of two-dimensional {Lorenz} transformations},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
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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/