Volume preserving bi-Lipschitz homeomorphisms on the Heisenberg group
Symplectic Geometry
2007-05-23 v2 Metric Geometry
Abstract
Elementary sub-Riemannian geometry on the Heisenberg group H(n) provides a compact picture of symplectic geometry. Any Hamiltonian diffeomorphism on lifts to a volume preserving bi-Lipschitz homeomorphisms of H(n), with the use of its generating function. Any curve of a flow of such homeomorphisms deviates from horizontality by the Hamiltonian of the flow. From the metric point of view this means that any such curve has Hausdorff dimension 2 and the (area) density equal to the Hamiltonian. The non-degeneracy of the Hofer distance is a direct consequence of this fact.
Keywords
Cite
@article{arxiv.math/0205039,
title = {Volume preserving bi-Lipschitz homeomorphisms on the Heisenberg group},
author = {Marius Buliga},
journal= {arXiv preprint arXiv:math/0205039},
year = {2007}
}