Abstract
A point q in a contact manifold (M, ξ) 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.
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Sandon, S. A Morse estimate for translated points of contactomorphisms of spheres and projective spaces. Geom Dedicata 165, 95–110 (2013). https://doi.org/10.1007/s10711-012-9741-1
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DOI: https://doi.org/10.1007/s10711-012-9741-1