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In this article we consider a variant of Rabinowitz Floer homology in orderto define a homological count of discriminant points for paths ofcontactomorphisms. The growth rate of this count can be seen as an analogue ofGivental's nonlinear Maslov index. As an application we prove a Bott-Samelsontype obstruction theorem for positive loops of contactomorphisms.

A variational approach to Givental's nonlinear Maslov index