Gary R. Nicklason
We consider the classical Poincare problem
where are homogeneous polynomials of degree . Associated with this system is an Abel differential equation
in which the coefficients are trigonometric polynomials. We investigate two separate conditions which produce a constant first absolute invariant of this equation. One of these conditions leads to a new class of integrable, center conditions for the Poincare problem if is an odd integer. We also show that both classes of solutions produce polynomial solutions to the problem.
Submitted June 7, 2010. Published September 14, 2010.
Math Subject Classifications: 34A05, 34C25.
Key Words: Center-focus problem; Abel differential equation; constant invariant; symmetric centers.
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| Gary R. Nicklason |
Mathematics, Physics and Geology
Cape Breton University
Sydney, Nova Scotia, Canada B1P 6L2
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