6533b826fe1ef96bd1283dab

RESEARCH PRODUCT

Principal Poincar\'e Pontryagin Function associated to some families of Morse real polynomials

M UribeM Pelletier

subject

Abelian integralPure mathematicsLogarithmApplied Mathematics34M35 34C08 14D05General Physics and AstronomyStatistical and Nonlinear PhysicsMorse codelaw.inventionPontryagin's minimum principlesymbols.namesakeMonodromylawPoincaré conjecturesymbolsPoint at infinitySpecial caseMathematics - Dynamical SystemsMathematical PhysicsMathematics

description

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.

yearjournalcountryeditionlanguage
2014-01-17
10.1088/0951-7715/27/2/257http://arxiv.org/abs/1303.1729