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math.DG2024
Generalizing Hamiltonian Mechanics with Closed Differential Forms
Nathan Duignan, Naoki Sato
Classical Hamiltonian mechanics, characterized by a single conserved Hamiltonian (energy) and symplectic geometry, `hides' other invariants into symmetries of the Hamiltonian or in…
math-ph2024
Global realisation of magnetic fields as 1D Hamiltonian systems
Nathan Duignan, David Perrella, David Pfefferlé
The paper reviews the notion of D non-autonomous Hamiltonian systems, portraying their dynamics as the flow of the Reeb field related to a closed two-form of maximal…