arXiv subjects

Viktor Ginzburg

Publications and source records attributed to Viktor Ginzburg.

3 recordsLinked to original sources

arXiv2004

Energy capacity inequalities via an action selector

An action selector associates, in a suitable way, to each compactly supported Hamiltonian on a symplectic manifold an action value of the Hamiltonian. Action selectors are known to exist for a broad class of symplectic manifolds. We show how the existence of an action selector leads to sharp energy capacity inequalities between the Gromov width, the Hofer--Zehnder capacity, and the displacement energy. We also obtain sharp lower bounds for the smallest action of a closed characteristic on contact type hypersurfaces.

math.DG↗

arXiv2004

Existence of relative periodic orbits near relative equilibria

We show existence of relative periodic orbits (a.k.a. relative nonlinear normal modes) near relative equilibria of a symmetric Hamiltonian system under an appropriate assumption on the Hessian of the Hamiltonian. This gives a relative version of the Moser-Weinstein theorem. The paper supersedes an earlier paper (this arxiv math.SG/9906007), which contains a mistake.

math.SG↗

arXiv1996

Cobordism theory and localization formulas for Hamiltonian group actions

We announce the following result and give several applications: A Hamiltonian $T$-space (for $T$ a torus) with isolated fixed points is cobordant to a disjoint union of weighted projective spaces which are constructed from its fixed point data. The applications concern the Duistermaat-Heckman formula, the topological Jeffrey-Kirwan localization theorem, and geometric quantization.

dg-ga↗