Entropy of semiclassical measures in dimension 2
Rivière, Gabriel
Duke Math. J., Tome 151 (2010) no. 1, p. 271-335 / Harvested from Project Euclid
We study the high-energy asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface $M$ of Anosov type. To do this, we look at families of distributions associated to them on the cotangent bundle $T^*M$ and we derive entropic properties on their accumulation points in the high-energy limit (the so-called semiclassical measures). We show that the Kolmogorov-Sinai entropy of a semiclassical measure $\mu$ for the geodesic flow $g^t$ is bounded from below by half of the Ruelle upper bound; that is, \[h_{KS}(\mu,g)\geq \frac{1}{2}\int_{S^*M} \chi^+(\rho)\ d\!\mu(\rho),\] where $\chi^+(\rho)$ is the upper Lyapunov exponent at point $\rho$ .
Publié le : 2010-11-01
Classification:  32F32,  53C21,  53C20
@article{1288185457,
     author = {Rivi\`ere, Gabriel},
     title = {Entropy of semiclassical measures in dimension 2},
     journal = {Duke Math. J.},
     volume = {151},
     number = {1},
     year = {2010},
     pages = { 271-335},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1288185457}
}
Rivière, Gabriel. Entropy of semiclassical measures in dimension 2. Duke Math. J., Tome 151 (2010) no. 1, pp.  271-335. http://gdmltest.u-ga.fr/item/1288185457/