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Pseudo-Abelian integrals on slow-fast Darboux systems
Marcin Bobienski, Pavao Mardesic, Dmitry Novikov
We study pseudo-Abelian integrals associated with polynomial deformations of slow-fast Darboux integrable systems. Under some assumptions we prove local boundedness of the number o…
Pseudo-Abelian integrals: unfolding generic exponential case
Marcin Bobienski, Pavao Mardesic, Dmitry Novikov
We consider an integrable polynomial system with generalized Darboux first integral H_0. We assume that it defines a family of real cycles in a region bounded by a polycycle. To an…
A counterexample to a multidimensional version of the weakened Hilbert's 16-th problem
Marcin Bobienski, Henryk Zoladek
In the weakened 16th Hilbert's Problem one asks for a bound of the number of limit cycles which appear after a polynomial perturbation of a planar polynomial Hamiltonian vector fie…
Contour integrals as -invariant functions on the fundamental group
Marcin Bobienski
We introduce a general approach to contour integrals. It covers usual Abelian integrals, the higher order Melnikov integrals and the generalized Abelian integrals. We prove that th…