On the non-persistence of Hamiltonian identity cycles

Details On the non-persistence of Hamiltonian identity cycles On the non-persistence of Hamiltonian identity cycles

2008-05-30

arxiv.org/abs/0806.0017v1

J. Differential Equations 246 (2009) 2706-2723

Mathematics

Dynamical Systems

17 pages

Scientific paper

We study the leading term of the holonomy map of a perturbed plane polynomial Hamiltonian foliation. The non-vanishing of this term implies the non-persistence of the corresponding Hamiltonian identity cycle. We prove that this does happen for generic perturbations and cycles, as well for cycles which are commutators in Hamiltonian foliations of degree two. Our approach relies on the Chen's theory of iterated path integrals which we briefly resume.

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