Phase Portraits on the Poincaré disk of linear type centers of Hamiltonian systems of degree five [ Back ]

Date:
12.06.17   
Times:
15:30
Place:
UAB - Dept. Matemàtiques (C1/-128)
Speaker:
Y. Paulina Martínez
University:
Universidad del Bío-Bío

Abstract

We show the phase portraits on the Poincaré disk for linear type centers of polynomial Hamiltonian systems of degree 4 of two types of Hamiltonian functions in terms of its parameters. We consider $H (x,y) =H_1(x) + H_2(y)$, where $H_1(x) = 1/2x^2+ a_3/3 x^3 + a_4/4 x_4 + a_5/5 x^5$ and $H_2 (y ) = 1/2 y_2 +b_3/3 y^3 + b_4/4 y^4 + b_5^5 y^5$ with $a_5 b_5 \neq 0$, and $H(x,y) = 1/2(x^2 + y^2) + a x^4y + b x^2y^3 + c y^5$.