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Convex integration and the holonomic approximation theorem are two well-known pillars of flexibility in differential topology and geometry. They may each seem to have their own flavor and scope. The goal of this paper is to bring some new perspective on this topic. We explain how to prove the holonomic approximation theorem for first-order jets using convex integration. More precisely, we first prove that this theorem can easily be reduced to proving flexibility of some specific relation. Then we prove this relation is open and ample, hence its flexibility follows from off-the-shelf convex integration. [ABSTRACT FROM AUTHOR]

We give examples of contactomorphisms in every dimension that are smoothly isotopic to the identity but that are not contact isotopic to the identity. In fact, we prove the stronger statement that they are not even symplectically pseudo-isotopic to the identity. We also give examples of pairs of contactomorphisms which are smoothly conjugate to each other but not by contactomorphisms. [ABSTRACT FROM AUTHOR]