Scarcity of periodic orbits in outer billiards. (arXiv:1706.03882v1 [math.DS])

We give a simple proof of our previous result with V. Zharnitsky that the set of period 4 orbits in planar outer billiard with piecewise smooth convex boundary has empty interior, provided that no four corners of the boundary form a parallelogram. We also obtain results on period 5 and 6 orbits. 查看全文>>