A Morse estimate for translated points of contactomorphisms of spheres and projective spaces

Abstract

A point q in a contact manifold is called a translated point for a contactomorphism ϕ, with respect to some fixed contact form, if ϕ(q) and q belong to the same Reeb orbit and the contact form is preserved at q. In this article we discuss a version of the Arnold conjecture for translated points of contactomorphisms and, using generating functions techniques, we prove it in the case of spheres (under a genericity assumption) and projective spaces.

14 pages; revised version, to appear in Geom. Dedicata

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