location:  Publications → journals
Search results

Search: All articles in the CJM digital archive with keyword billiards

 Expand all        Collapse all Results 1 - 2 of 2

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, HausdorffCategories:37D20, 37D40

2. CJM 2011 (vol 64 pp. 1058)

Plakhov, Alexander
 Optimal Roughening of Convex Bodies A body moves in a rarefied medium composed of point particles at rest. The particles make elastic reflections when colliding with the body surface, and do not interact with each other. We consider a generalization of Newton's minimal resistance problem: given two bounded convex bodies $C_1$ and $C_2$ such that $C_1 \subset C_2 \subset \mathbb{R}^3$ and $\partial C_1 \cap \partial C_2 = \emptyset$, minimize the resistance in the class of connected bodies $B$ such that $C_1 \subset B \subset C_2$. We prove that the infimum of resistance is zero; that is, there exist "almost perfectly streamlined" bodies. Keywords:billiards, shape optimization, problems of minimal resistance, Newtonian aerodynamics, rough surfaceCategories:37D50, 49Q10