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October 9, 2025Open Access

Direct Products for the Hamiltonian Density Property

Key Points

The direct product of two Stein manifolds retains the hamiltonian density property, indicating a robust structural feature.
Relations between the hamiltonian density property and the symplectic density property provide new insights into manifold structures.
The properties are successfully established for $(\mathbb{C}^\ast)^{2n}$ and traceless Calogero--Moser spaces, marking significant findings.
A Carleman-type approximation for hamiltonian diffeomorphisms showcases the practical application of these theoretical results.

Abstract

We show that the direct product of two Stein manifolds with the Hamiltonian density property enjoys the Hamiltonian density property as well. We investigate the relation between the Hamiltonian density property and the symplectic density property. We then establish the Hamiltonian and the symplectic density property for (C^) ^2n and for the so-called traceless Calogero--Moser spaces. As an application we obtain a Carleman-type approximation for Hamiltonian diffeomorphisms of a real form of the traceless Calogero--Moser space.

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