C^0-limits of Hamiltonian paths and the Oh-Schwarz spectral invariants

Details C^0-limits of Hamiltonian paths and the Oh-Schwarz spectral invariants C^0-limits of Hamiltonian paths and the Oh-Schwarz spectral invariants

2011-09-19

arxiv.org/abs/1109.4123v1

Mathematics

Symplectic Geometry

32 pages

Scientific paper

In this article we study the behavior of the Oh-Schwarz spectral invariants under C^0-small perturbations of the Hamiltonian flow. We obtain an estimate, which under certain assumptions, relates the spectral invariants of a Hamiltonian to the C^0-distance of its flow from the identity. Using the mentioned estimate we show that, unlike the Hofer norm, the spectral norm is C^0-continuous on surfaces. We also present applications of the above results to the theory of Calabi quasimorphisms and improve a result of Entov, Polterovich and Py. In the final section of the paper we use our results to answer a question of Y.-G. Oh about spectral Hamiltonian homeomorphisms.

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