All Questions

Let $X$ be the Hopf vector field on the three-sphere. Is there a smooth nowhere zero function $f$ so that the modified vector field $fX$ is not the Reeb vector field of any contact form on the three-...

Is there an example of a smooth vector field $v$ on $S^3$ such that $v$ preserves a volume form and $v$ is not a Reeb vector field? Recall that $v$ is a Reeb vector field if there exists a contact $...

I'm looking for examples that highlight how dynamical systems (particularly, Hamiltonian and Reeb dynamics) can be used to shed light in other areas of mathematics. This could potentially include ...

Let us assume someone is interested in the study of Hamiltonian mechanics. What are good examples to illustrate him of the usefulness of contact geometry in this context? On one hand the Hamiltonian ...