ABSTRACT
Note that if we fix the homotopy class of a map u satisfying (5.6) we ca define A h (x +) — A h ( x - ) as
R e m a r k : v(\\H\\co,P) actually depends only on | | # | |c ° a^d the smallest area of a holomorphic sphere in P for some almost complex structure. In particular, if we call a(P, J) this area, we can assume
In this paper we tried to convey the feeling that periodic orbits of au tonomous Hamiltonian systems are important in several ways, and to show some new techniques that have been successful in dealing with them. We saw in section 4 that, as far as symplectic geometry is concerned, periodic orbits obviously appear in the Weinstein conjecture, hence in the structure of contact manifolds, but also, less obviously when dealing with lagrangian em b ed d in g s. In fact these can be co n sid ered as the two extremes of the following conjecture that we would like to give as a conclusion:
