Geodesic
The Hausdorff Dimension of an Ergodic Invariant Measure for a Piecewise Monotonic Map of the Interval
Canadian mathematical bulletin, Tome 35 (1992) no. 1, pp. 84-98

Voir la notice de l'article provenant de la source Cambridge University Press

We consider a piecewise monotonie and piecewise continuous map T on the interval. If T has a derivative of bounded variation, we show for an ergodic invariant measure μ with positive Ljapunov exponent λμ that the Hausdorff dimension of μ equals hμ / λμ.
DOI : 10.4153/CMB-1992-013-x
Mots-clés : 28D05. 
Hofbauer, Franz. The Hausdorff Dimension of an Ergodic Invariant Measure for a Piecewise Monotonic Map of the Interval. Canadian mathematical bulletin, Tome 35 (1992) no. 1, pp. 84-98. doi: 10.4153/CMB-1992-013-x
@article{10_4153_CMB_1992_013_x,
     author = {Hofbauer, Franz},
     title = {The {Hausdorff} {Dimension} of an {Ergodic} {Invariant} {Measure} for a {Piecewise} {Monotonic} {Map} of the {Interval}},
     journal = {Canadian mathematical bulletin},
     pages = {84--98},
     year = {1992},
     volume = {35},
     number = {1},
     doi = {10.4153/CMB-1992-013-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1992-013-x/}
}
TY  - JOUR
AU  - Hofbauer, Franz
TI  - The Hausdorff Dimension of an Ergodic Invariant Measure for a Piecewise Monotonic Map of the Interval
JO  - Canadian mathematical bulletin
PY  - 1992
SP  - 84
EP  - 98
VL  - 35
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1992-013-x/
DO  - 10.4153/CMB-1992-013-x
ID  - 10_4153_CMB_1992_013_x
ER  - 
%0 Journal Article
%A Hofbauer, Franz
%T The Hausdorff Dimension of an Ergodic Invariant Measure for a Piecewise Monotonic Map of the Interval
%J Canadian mathematical bulletin
%D 1992
%P 84-98
%V 35
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1992-013-x/
%R 10.4153/CMB-1992-013-x
%F 10_4153_CMB_1992_013_x

[1] 1. Brin, M. and Katok, A., On local entropy. In Geometric Dynamics. Springer Lect. Notes Math. 1007,1983, 30–38. Google Scholar

[2] 2. Hofbauer, F., Piecewise invertible dynamical systems, Probab. Theory Relat. Fields 72(1986),359–386. Google Scholar

[3] 3. Keller, G., Lifting measures to Markov extensions, Monatsh. Math. 108(1989),183–200. Google Scholar

[4] 4. Ledrappier, F. and Misiurewicz, M., Dimension of invariant measures for maps with entropy zero, Ergodic Theory Dyn. Syst. 5(1985),595–610. Google Scholar

[5] 5. Raith, P., Hausdorff dimension for piecewise monotonie maps, Studia Math. 94(1989),17–33. Google Scholar

[6] 6. Young, L. S., Dimension, entropy and Ljapunov exponents, Ergodic Theory Dyn. Syst. 2(1982),109–124. Google Scholar

Cité par Sources :