Billiards in the l ^{ p } unit balls of the plane 

Division of Physics, Mathematics and Astronomy, Caltech Pasadena, CA, 91125, USA 
Jeng's work was supported by a SURF Undergraduate Research Fellowship. 
This paper appeared in the journal Chaos, Fractals and Solitons, Vol. 7, p. 543554, 1996 
Abstract 
We study a oneparameter family of billiard maps given by the convex tables for . Using results of Mather, Hubacher and Angenent, we note that the topological entropy is positive if . We study the linear stability of some periodic orbits and observe that the stability of these orbits changes for p=2. For , there exist elliptic periodic orbits suggesting that is not ergodic for all p. We compute numerically the metric entropy of the maps in the interval [1,12] and the limiting behaviour near p =2. 
