On cosymplectic dynamics. I. (Q2671428)

The paper under review is an introduction to cosymplectic topology. By adapting methods from symplectic topology, the authors characterize and study several subgroups of diffeomophisms of a cosymplectic manifold. Recall that a cosymplectic structure on a smooth manifold is given by a closed \(2\)-form \(\omega\) and a closed \(1\)-form \(\eta\) such that \(\eta \wedge \omega\) is a nowhere vanishing top-form. In particular, among many other results, the authors show that the Reeb vector field determines the almost cosymplectic nature of a uniform limit of a sequence of almost cosymplectic diffeomorphisms. They also define and study the cosymplectic setting of Hofer and Hofer-like geometries with respect to the group of all cosymplectic diffeomorphisms isotopic to the identity map.