Defeito zero para bilhares convexos em H2

Abstract

Let Q be a strictly geodesically convex region in the hyperbolic plane bounded by a closed curve with strictly positive geodesic curvature. A billiard on Q consists in the particle’s free motion suffering elastic collisions with the boundary of the region. On this tesis, we will show that, generically, a periodic trajectory do not hit multiple times a same point with distinct angles. Additionally, we will show that, generically, two distinct periodic orbits and with same period do not have common points. The main tool we use is Thom’s transversality theorem on multijets of functions in C∞emb (T, H2 ).