Principal Poincar\'e Pontryagin Function associated to some families of Morse real polynomials
Dynamical Systems
2015-06-15 v1
Abstract
It is known that the Principal Poincar\'e 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 Poincar\'e 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.
Keywords
Cite
@article{arxiv.1303.1729,
title = {Principal Poincar\'e Pontryagin Function associated to some families of Morse real polynomials},
author = {Michele Pelletier and Marco Uribe},
journal= {arXiv preprint arXiv:1303.1729},
year = {2015}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1104.4021