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RESEARCH PRODUCT

Perturbations of symmetric elliptic Hamiltonians of degree four

Pavao MardešićChengzhi LiRobert Roussarie

subject

Chebychev propertyDegree (graph theory)Applied MathematicsMathematical analysisBifurcation diagramAnnulus (mathematics)Unfolding symmetric Hamiltonian systemsParameter spaceBifurcation diagramMelnikov functionsunfolding symmetric Hamiltonian systems; Melnikov functions; Chebychev property; Bifurcation diagramDisplacement functionPrincipal partLimit (mathematics)AnalysisSign (mathematics)Mathematics

description

AbstractIn this paper four-parameter unfoldings Xλ of symmetric elliptic Hamiltonians of degree four are studied. We prove that in a compact region of the period annulus of X0 the displacement function of Xλ is sign equivalent to its principal part, which is given by a family induced by a Chebychev system; and we describe the bifurcation diagram of Xλ in a full neighborhood of the origin in the parameter space, where at most two limit cycles can exist for the corresponding systems.

yearjournalcountryeditionlanguage
2006-12-01Journal of Differential Equations
10.1016/j.jde.2006.07.016http://dx.doi.org/10.1016/j.jde.2006.07.016