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math.DS2026
Breaking of invariant curves: from the Fermi-Ulam map to the breathing circle billiard
José Lamas, Stefano Marò
We consider the breathing circle billiard, in which a point particle moves freely inside a disk. The radius varies periodically in time, with elastic reflections at the moving boun…
math.SG2026
Birkhoff normal forms, Dirac brackets and symplectic reduction
Jose Lamas, Lei Zhao
Dirac brackets are widely used to study constrained Hamiltonian dynamics. In this paper we develop a Dirac-bracket approach to normal forms on momentum levels and relate it to symp…