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This note on the flux homomorphism for strictly contact isotopies complementsthe recent paper [MS11a] by P. Spaeth and the author. We determine the volumeflux restricted to symplectic and volume-preserving contact isotopies and theirC^0-limits for some classes of symplectic and contact manifolds and for anumber of examples. In particular, we see that the restriction of the flux mayfail to be surjective. It vanishes for an isotopy preserving a regular contactform, but can be nontrivial for non-regular contact forms. Applications arediscussed in the article cited above. We also find obstructions to regularizinga strictly contact isotopy that are not present for Hamiltonian isotopies[Pol01, Section 5.2] or contact isotopies [MS11b].

A note on the volume flux of smooth and continuous strictly contact isotopies