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

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1. CJM 2016 (vol 69 pp. 532)

Ganguly, Arijit; Ghosh, Anish
Dirichlet's Theorem in Function Fields
We study metric Diophantine approximation for function fields specifically the problem of improving Dirichlet's theorem in Diophantine approximation.

Keywords:Dirichlet's theorem, Diophantine approximation, positive characteristic
Categories:11J83, 11K60, 37D40, 37A17, 22E40

2. 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

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