CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  Publicationsjournals
Publications        
Search results

Search: MSC category 37D40 ( Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) )

  Expand all        Collapse all Results 1 - 1 of 1

1. CJM 2013 (vol 65 pp. 1384)

Wright, Paul
Estimates of Hausdorff Dimension for Non-wandering Sets of Higher Dimensional Open Billiards
This article concerns a class of open billiards consisting of a finite number of strictly convex, non-eclipsing obstacles $K$. The non-wandering set $M_0$ of the billiard ball map is a topological Cantor set and its Hausdorff dimension has been previously estimated for billiards in $\mathbb{R}^2$, using well-known techniques. We extend these estimates to billiards in $\mathbb{R}^n$, and make various refinements to the estimates. These refinements also allow improvements to other results. We also show that in many cases, the non-wandering set is confined to a particular subset of $\mathbb{R}^n$ formed by the convex hull of points determined by period 2 orbits. This allows more accurate bounds on the constants used in estimating Hausdorff dimension.

Keywords:dynamical systems, billiards, dimension, Hausdorff
Categories:37D20, 37D40

© Canadian Mathematical Society, 2014 : https://cms.math.ca/