Hitting time and dimension in Axiom A systems and generic interval excanges
Galatolo, Stefano
arXiv, 0506516 / Harvested from arXiv
Text on arXiv
In this note we prove that for equilibrium states of axiom A systems the time $\tau_{B}(x)$ needed for a typical point $x$ to enter for the first time in a typical ball $B$ with radius $r$ scales as $\tau_{B}(x)\sim r^{d}$ where $d$ is the local dimension of the invariant measure at the center of the ball. A similar relation is proved for a full measure set of interval excanges. Some applications to Birkoff averages of unbounded (and not $L^{1}$) functions are shown.
Publié le : 2005-06-24
Classification:  Mathematics - Dynamical Systems,  Mathematical Physics,  37B20,  37C45,  37D20 
@article{0506516,
     author = {Galatolo, Stefano},
     title = {Hitting time and dimension in Axiom A systems and generic interval
  excanges},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0506516}
}

Galatolo, Stefano. Hitting time and dimension in Axiom A systems and generic interval
  excanges. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0506516/