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math.DS2021★ 1 cited
Non co-preservation of the & -rational caustics along deformations of circles
V. Kaloshin, C. E. Koudjinan
For any given positive integer , we prove that every plane deformation of a circle which preserves the and -rational caustics is trivial i.e. the deformation con…
math.DS2021
On some invariants of Birkhoff billiards under conjugacy
V. Kaloshin, C. E. Koudjinan
In the class of strictly convex smooth boundaries, each of which not having strip around its boundary foliated by invariant curves, we prove that the Taylor coefficients of the "no…