Sure plays a mean pinball

Pinball Scattering

Classical and semiclassical periodic orbit expansions are applied to the dynamics of a point particle scattering elastically oo several disks in a plane. Fredholm determinants, zeta functions, and convergence of their cycle expansions are tested and applied to evaluation of classical escape rates and quantum resonances. The results demonstrate applicability of the Ruelle and Gutzwiller type per...

A lost "pinball" in the left atrium.

Google PageRank as mean playing time for pinball on the reverse web

It is known that the output from Google’s PageRank algorithm may be interpreted as (a) the limiting value of a linear recurrence relation that is motivated by interpreting links as votes of confidence, and (b) the invariant measure of a teleporting random walk that follows links except for occasional uniform jumps. Here, we show that, for a sufficiently frequent jump rate, the PageRank score ma...

A framework of iterative learning control under random data dropouts: Mean square and almost sure convergence

This paper addresses the iterative learning control problem under random data dropout environments. The recent progress on iterative learning control in the presence of data dropouts is first reviewed from 3 aspects, namely, data dropout model, data dropout position, and convergence meaning. A general framework is then proposed for the convergence analysis of all 3 kinds of data dropout models,...

Pinball billiards with dominated splitting

We study the dynamics of a type of nonconservative billiards where the ball is “kicked” by the wall giving a new impulse in the direction of the normal. For different types of billiard tables we study the existence of attractors with dominated splitting.