Timeline for Obstructions for finding a volume form for a given flow
Current License: CC BY-SA 4.0
3 events
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| Oct 29, 2019 at 0:51 | comment | added | Daniel Asimov | Tali — Multiplying a (smooth) vector field by a positive (smooth) function is only one of several ways to possibly obtain another vector field with equivalent orbits. For instance, for any "structurally stable" vector field V in the sense of Smale after undergoing a sufficiently small C<sup>1</sup> perturbation will result in a field V' that is orbit equivalent to V. But be aware that the equivalence may be only by a homeomorphism, and not a diffeomorphism, of the underlying manifold that is close to the identity. Another way is to carry V to a new one V' by any diffeomorphism of the manifold. | |
| Apr 30, 2019 at 8:08 | comment | added | Tali | Thanks a lot Alejandro. One more question: I'm actually interested in the flow (induced by the vector field) up to orbit equivalence. I think this is equivalent to saying that the vector field can be multiplied by a positive function. Would it then be easier to give a topological charecterization (hopefully something like there are no transverse surfaces)? | |
| Apr 28, 2019 at 22:01 | history | answered | Alejandro | CC BY-SA 4.0 |