TY - JOUR
T1 - Differentiability of hausdorff dimension of the non-wandering set in a planar open billiard
AU - Wright, Paul
PY - 2016/7
Y1 - 2016/7
N2 - We consider open billiards in the plane satisfying the no-eclipse condition. We show that the points in the non-wandering set depend differentiably on deformations to the boundary of the billiard. We use Bowen's equation to estimate the Hausdorff dimension of the non-wandering set of the billiard. Finally we show that the Hausdorff dimension depends differentiably on sufficiently smooth deformations to the boundary of the billiard, and estimate the derivative with respect to such deformations.
AB - We consider open billiards in the plane satisfying the no-eclipse condition. We show that the points in the non-wandering set depend differentiably on deformations to the boundary of the billiard. We use Bowen's equation to estimate the Hausdorff dimension of the non-wandering set of the billiard. Finally we show that the Hausdorff dimension depends differentiably on sufficiently smooth deformations to the boundary of the billiard, and estimate the derivative with respect to such deformations.
UR - https://www.scopus.com/pages/publications/84962590141
U2 - 10.3934/dcds.2016.36.3993
DO - 10.3934/dcds.2016.36.3993
M3 - Article
SN - 1078-0947
VL - 36
SP - 3993
EP - 4014
JO - Discrete and Continuous Dynamical Systems- Series A
JF - Discrete and Continuous Dynamical Systems- Series A
IS - 7
ER -