TITLE:
Singular phenomena for convex billiard tables

AUTHORS:
Rafael Ramirez-Ros

Departament de Matematica Aplicada I 
Universitat Politecnica de Catalunya
Diagonal 647, 08028 Barcelona, Spain
E-mails: rafael@vilma.upc.edu

ABSTRACT:
The splitting of separatrices of area-preserving maps close to the 
identity is one of the most paradigmatic examples of 
exponentially small or singular phenomenon.
We present a couple of numerical results in this frame 
for billiards inside perturbed almost-circular ellipses.
Firstly, the validity of some singular Melnikov predictions for the 
splitting size is established.
Secondly, some singular bifurcations on the number of primary
homoclinic trajectories are also described.

KEYWORDS:
Billiards, separatrix splitting, Melnikov method, singular phenomena