Outer Billiards and Symplectic GeometrySharipova, Anastasiia symplectic geometryclosed characteristicsouter billiardsViterbo’s conjectureIvrii's conjectureperiodic orbitssymplectic billiardsMathematicsPHDIn this dissertation we study questions in the intersection of symplectic geometry, convex geometry and billiard dynamical systems. We get a new characterization of a ball in terms of Hamiltonian and outer billiard dynamics: we show that smooth and strongly convex bodies in the symplectic R^2n for n > 1 with all characteristics planar, or all outer billiard trajectories planar are affine symplectic images of balls. We also study questions about periodic billiard orbits and give a proof for (2n + 1, n) and (2n, n − 1)-periodic Ivrii’s conjecture for planar outer billiards. In addition, we give new simple geometric proofs for the 3 and 4-periodic cases for outer and symplectic billiards, and generalize for higher dimensions in case of symplectic billiards.Pierre-Emmanuel Jabin, Program Head/ChairLuen-Chau Li, Major Field MemberAnton Petrunin, Major Field MemberSergei Tabachnikov, Chair & Dissertation AdvisorMark Latash, Outside Unit & Field Memberopen_access2025-03-01T23:40:02Zhttps://etda.libraries.psu.edu/catalog/21743afs6172