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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.AP2024
Steady Compressible 3D Euler Flows in Toroidal Volumes without Continuous Euclidean Isometries
Naoki Sato, Michio Yamada
We demonstrate the existence of smooth three-dimensional vector fields where the cross product between the vector field and its curl is balanced by the gradient of a smooth functio…