On the adjoint action of the group of symplectic diffeomorphisms

DOI10.4310/PAMQ.2022.V18.N2.A14arXiv2009.06729MaRDI QIDQ6349084

László Lempert

Publication date: 14 September 2020

Abstract: We study the action of Hamiltonian diffeomorphisms of a compact symplectic manifold ($X,omega$) on $C^{i}nfty(X)$ and on functions $C^{i}nfty(X)omathbbR$. We describe various properties of invariant convex functions on $C^{i}nfty(X)$. Among other things we show that continuous convex functions $C^{i}nfty(X)omathbbR$ that are invariant under the action are automatically invariant under so called strict rearrangements and they are continuous in the sup norm topology of $C^{i}nfty(X)$; but this is not generally true if the convexity condition is dropped.

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Contact manifolds (general theory) (53D10) Canonical transformations in symplectic and contact geometry (53D22) Symplectic and canonical mappings (37J11)

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