0000000000636767

AUTHOR

Henryk Zoladek

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A note on higher order Melnikov functions

2005

We present several classes of planar polynomial Hamilton systems and their polynomial perturbations leading to vanishing of the first Melnikov integral. We discuss the form of higher order Melnikov integrals. In particular, we present new examples where the second order Melnikov integral is not an Abelian integral.

Abelian integralPolynomialPure mathematicsMathematics::Dynamical SystemsApplied MathematicsMathematical analysisMathematics::Classical Analysis and ODEsPhysics::Fluid DynamicsNonlinear Sciences::Chaotic DynamicsPlanarDiscrete Mathematics and CombinatoricsOrder (group theory)Nonlinear Sciences::Pattern Formation and SolitonsMathematicsQualitative Theory of Dynamical Systems
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