| Abstract: |
| A point mass moves inside a planar convex domain under the gravitational attraction of a fixed positive mass. Upon reaching the boundary, the particle is reflected back inside the domani according to the geometric optics law: the angle of incidence equals the angle of reflection. It is known that this dynamical system is integrable (for all energy levels) when for instance the boundary is an ellipse and the attracting mass is placed at one of its foci.
In this talk we will discuss the following rigidity phenomenon: among analytic, centrally symmetric, compact convex domains, the only ones for which the corresponding Kepler billiard is analytically integrable (at least for sufficiently large energies) are circles with the attracting mass placed at their centres and ellipses, with the attracting mass at a focus. Our approach is based on an explicit construction of a symbolic dynamics for the system. |
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