Investigation of trajectories in various classes of billiards

ABSTRACTPhD. ThesisINVESTIGATION OF TRAJECTORIESIN VARIOUS CLASSES OF BILLIARDS˙ ˙ALI DENIZAnadolu UniversityGraduate School of SciencesMathematics Program˙Supervisor: Assist.Prof.Dr. Andrei RATIU2005, 75 PagesThe trajectories in various classes of plane and space billiardsare investigated. In the second chapter one is concerned with theproblem of the existence of periodical trajectories in polygonal bil-liards. Trajectories ressembling to the classical Fagnano orbit areconstructed in cyclic quadrilaterals and in 2n-gons. In the thirdchapter a series of results on trajectories in smooth convex billiardsand projective billiards are considered. Moreover a newly intro-duced family of convex billiards with bouncing law defined by twocertain gradient vector fields on the boundary are being studied inthis chapter. Finally, in the fourth chapter, the class of open bil-liards (i.e. billiards with obstacles) is considered in the Euclidean aswell as hyperbolic space, and one proves that there is a trajectoryhitting the obstacles in any given order.Keywords : Billiard trajectories, Polygonal billiards, Convex billiards,Projective billiards, Open billiards