| Abstract: |
| We investigate the integrability of Kepler billiards-mechanical billiard systems in
which a particle moves under the influence of a Keplerian potential and reflects elastically at the
boundary of a strictly convex planar domain. Our main result establishes that, except possibly
for one location of the gravitational center, analytic integrability at high energies occurs only
when the domain is an ellipse and the center is placed at one of its foci. This provides a partial
affirmative answer to a Keplerian analogue of the classical Birkhoff-Poritsky Conjecture.
Our approach is based on the construction of symbolic dynamics arising from chaotic subsys-
tems that emerge in the high-energy regime. |
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