Variations at infinity in contact form geometry

Let v be a nonsingular Morse–Smale vector field in the kernel of a contact form α, with Reeb vector field , defined on M³. We establish that the associated variational problem at infinity defined by the action functional on the stratified space of curves made of -pieces of orbits alternating with -pieces of orbits satisfies the Palais–Smale condition. This result takes a more special form for the standard contact structure of S³. Dedicated to Felix Browder on his eightieth birthday