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Completeness of Hamiltonian vector fields in Jacobi and contact geometry. (English) Zbl 1240.53145

Summary: The completeness of the Hamiltonian vector fields in the Jacobi manifolds is studied here providing a sufficient condition in terms of the topological properness for a function assuring a sublinear growth along the flow. In particular, the settings of Poisson, contact and cosymplectic geometries are presented while for similarities with the Poisson case, the Nambu-Poisson structures are included too. As applications, the completeness of contact-Hamiltonian vector fields arising in the geometrization of thermodynamics is discussed with examples.

MSC:

53D15 Almost contact and almost symplectic manifolds
53D17 Poisson manifolds; Poisson groupoids and algebroids
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