An obstruction to conservation of volume in contact dynamics

Details An obstruction to conservation of volume in contact dynamics An obstruction to conservation of volume in contact dynamics

2000-09-26

arxiv.org/abs/math/0009227v1

Mathematics

Symplectic Geometry

Latex, 14 pages, preliminary version

Scientific paper

A theorem of Moser guarantees that every diffeomorphism of a closed manifold can be isotoped to a volume preserving one. We show that this statement cannot be extended into contact category: some connected components of contactomorphism groups of certain contact manifolds contain no volume-preserving diffeomorphisms. This phenomenon can be considered from different viewpoints: geometric (isometric action of the contact mapping class group on the moduli space of contact forms), topological (action in symplectic homology) and dynamical (diffusion). We define a numerical invariant - a kind of contact Lyapunov exponent - which leads to a quantitive version of the abovementioned result.

Affiliated with

Also associated with

No associations

Rating

An obstruction to conservation of volume in contact dynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An obstruction to conservation of volume in contact dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An obstruction to conservation of volume in contact dynamics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-482966