arXiv subjects
Publications and source records attributed to Thomas Dauer.
We consider the long time behavior of the trajectories of the discontinuous analog of the standard Chirikov map. We prove that for some values of parameters all the trajectories remains bounded for all time. For other set of parameters we provide an estimate for the escape rate for the trajectories and present a numerically supported conjecture for the actual escape rate.
Let x and y be points in a billiard table M that is bounded by a curve sigma. We assume that sigma is a simple closed C^r curve with positive curvature, where r is at least 2. A subset B of M\{x,y} is called a blocking set for the pair (x,y) if every billiard path in M from x to y passes through a point in B. If a finite blocking set exists, the pair (x,y) is called secure in M; if not, it is called insecure. We show that for the generic (in the sense of Baire category) curve sigma, the generic pair of interior points is insecure.