Integrable systems via polynomial inverse integrating factors

✍ Scribed by J. Chavarriga; J. Giné; M. Grau

• Publisher: Elsevier Science
• Year: 2002
• Tongue: French
• Weight: 142 KB
• Volume: 126
• Category: Article
• ISSN: 0007-4497
• DOI: 10.1016/s0007-4497(02)01111-9

✦ Synopsis

We study the integrability of two-dimensional autonomous systems in the plane of the form ẋ = -y + X s (x, y), ẏ = x + Y s (x, y), where X s (x, y) and Y s (x, y) are homogeneous polynomials of degree s with s 2. Writing this system in polar coordinates, we study the existence of polynomial inverse integrating factors and we give some related invariants, from which we can compute a formal first integral for the system. Finally, we give a family of systems with s = 4 and with a centre at the origin, via inverse integrating factors, in which radial and angular coefficients do not independently vanish in Lyapunov constants.