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

TL;DR

This paper proves a version of the Arnold conjecture for translated points of contactomorphisms on spheres and projective spaces using generating functions techniques, establishing lower bounds on the number of such points.

Contribution

It introduces a Morse estimate for translated points of contactomorphisms on spheres and projective spaces, extending Arnold's conjecture to contact topology.

Findings

Proves a Morse-type estimate for translated points

Establishes the Arnold conjecture in specific contact manifolds

Uses generating functions techniques for the proof

Abstract

A point q in a contact manifold is called a translated point for a contactomorphism \phi, with respect to some fixed contact form, if \phi(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.