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We use Floer homology to study the Hofer-Zehnder capacity of neighborhoodsnear a closed symplectic submanifold M of a geometrically bounded andsymplectically aspherical ambient manifold. We prove that, when the unit normalbundle of M is homologically trivial in degree dim(M) (for example, if codim(M)> dim(M)), a refined version of the Hofer-Zehnder capacity is finite for allopen sets close enough to M. We compute this capacity for certain tubularneighborhoods of M by using a squeezing argument in which the algebraicframework of Floer theory is used to detect nontrivial periodic orbits. As anapplication, we partially recover some existence results of Arnold forHamiltonian flows which describe a charged particle moving in a nondegeneratemagnetic field on a torus. We also relate our refined capacity to the study ofHamiltonian paths with minimal Hofer length.

Squeezing in Floer theory and refined Hofer–Zehnder capacities of sets near symplectic submanifolds