Degenerate Maxima in Hamiltonian Systems

Details Degenerate Maxima in Hamiltonian Systems Degenerate Maxima in Hamiltonian Systems

2009-12-31

arxiv.org/abs/1001.0184v1

Mathematics

Symplectic Geometry

13 pages

Scientific paper

In this paper we explore loops of non-autonomous Hamiltonian diffeomorphisms
with degenerate fixed maxima. We show that such loops can not have totally
degenerate fixed global maxima. This has applications for the Hofer geometry of
the group of Hamiltonians for certain symplectic 4 manifolds and also gives
criteria for certain 4 manifolds to be uniruled.

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