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Hofer’s length spectrum of symplectic surfaces

par Khanevsky, Michael
Référence Journal of Modern Dynamics, 9, page (219-235)
Publication Publié, 2015

Article révisé par les pairs

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Résumé :

Following a question of F. Le Roux, we consider a system of invariants lA: H1(M)→ ℝ of a symplectic surface M. These invariants compute the minimal Hofer energy needed to translate a disk of area A along a given homology class and can be seen as a symplectic analogue of the Riemannian length spectrum. When M has genus zero we also construct Hofer- and C0- continuous quasimorphisms Ham(M) →H1(M) that compute trajectories of periodic non-displaceable disks.