So, do I get this right: you can only call a map from X to Y an inclusion if dim(X)=dim(Y)? How would you call a map from a lower-dimensional space to a higher-dimensional space? Embedding? Immersion? Inclusion? ...?
I'm not sure whether my case would actually be a symplectization of a...
Is there then a possibility to define a map from the lower-dimensional space to the higher one? I'm basically considering time-dependent systems on a (2n+1)-dimensional contact manifold T*Q x R, and I want to include/embed (don't know what term to use) in a (2n+2)-dimensional symplectic...
Hi,
Suppose I have a space X with coordinates (x,y,z) and a space Y with coordinates (x,y,z,t), so that dim(Y)=dim(X)+1.
What is the difference between the projection (x,y,z,t)->(x,y,z) and the inclusion (x,y,z)->(x,y,z,t)? Are they each others inverses? Especially if x=x(t), y=y(t) and...
Why? By isotropy group at some point m\in M, I mean the {g\in G | g(m)=m}. In my result I find that dim(iso-group)=0, so it is discrete. As G=G^n, that means the isotropy group is a discrete (abelian) subgroup of G, which I kind of hoped to be isomorphic to Z^k.
Quick question:
Suppose I have a (transitive) R^n action on a manifold M. If the isotropy group of R^n is discrete, does that mean that it is automatically isomorphic to Z/kZ, with 0<=k<=n?
Basically, my discrete subgroup is a lattice then, right?
Thanks!
Yes, it's basically a Lagrangian system, so I have a tangent bundle, M=TQ, where Q is the base manifold with coordinates q, and TQ has coordinates (q,\dot{q}). For a time-dependent Lagrangian L:TQ x R -> R, the diffeomorphism is a map TQ x R -> TQ x R, right? If so, I think I might finally get...
Hello!
It's my first post here, as I am currently reading some material, but have not been able to really grasp it. Sorry, if this is a rather dumb question.
I have a dynamical system (Newtonian) that is defined on some manifold M times R (time-dependent system). Say that time is labeled...