Take the 2-minute tour ×  Hello everybody. For a purpose of
consolidation of some result I am trying to set down, I need to
construct an example to sustain the theory and I am looking for
symplectic and Hamiltonian diffeomorphisms. So does someone can
help me writing some non-trivial explicit examples of symplectic
and Hamiltonian diffeomorphisms on compact surface? (at least
examples for $S^2$ and $T^2$ ) NB : By surface I mean
2-dimensional manifold. Thanks a lot  share|improve this
question Sorry, what is a symplectic diffeomorphism on a
manifold on which you haven't specified a symplectic structure?
Do you mean a symplectic diffeomorphism of the cotangent bundle?
–  Qiaochu Yuan Jul 29 '11 at 15:45 The standard area forms on
the torus and $S^2$ are symplectic structures. I assume those
would be good for explicit examples. –  Elizabeth S. Q. Goodman
Jul 30 '11 at 8:24 In fact as long as you endow a symplectic
structure, it doesn't matter which one it is because they are
all isotopic up to a scaling. For ex