arXiv subjects

Marco Uribe

Publications and source records attributed to Marco Uribe.

2 recordsLinked to original sources

arXiv2013

The displacement map associated to polynomial perturbations of some nongeneric Hamiltonians

It is known that the Principal Poincaré Pontryagin Function is generically an Abelian integral. In non generic cases it is an iterated integral. In previous papers one of the authors gives a precise description of the Principal Poincaré Pontryagin Function, an iterated integral af length at most 2, involving a logarithmic function with only one ramification at a point at infinity. We show here that this property can be generalized to Hamiltonians having real points at infinity and satisfying some properties.

math.DS↗

arXiv2013

Principal Poincaré Pontryagin Function associated to some families of Morse real polynomials

It is known that the Principal Poincaré Pontryagin Function is generically an Abelian integral. We give a sufficient condition on monodromy to ensure that it is an Abelian integral also in non generic cases. In non generic cases it is an iterated integral. Uribe [17, 18] gives in a special case a precise description of the Principal Poincaré Pontryagin Function, an iterated integral of length at most 2, involving logarithmic functions with only one ramification at a point at infinity. We extend this result to some non isodromic families of real Morse polynomials.

math.DS↗