Separatrices splitting for Birkhoff's billiard in symmetric convex domain, closed to an ellipse.
An example of a convex domain on the plane with the phenomenon of the transversal intersection of separatrices of the corresponding billiard mapping is presented. This example is constructed as an analytic global symmetric perturbation of an ellipse and we investigate the global symmetric analytic perturbation of the integrable billiard mapping in the ellipse. We establish a theorem on the separatrices splitting of the perturbed billiard mapping and derive the asymptotic formulas for a homoclinic invariant as well as for a "principal" splitting angle of separatrices, arising from the hyperbolic fixed point of the mapping. (c) 1994 American Institute of Physics.
Tabanov
M. B.
MB
St. Petersburg State Academy of Aerospace Instrumentations, 67, Bolshaja Morskaja, 190000, St. Petersburg, Russia.