Given a system of two autonomous ordinary differential equations whose right-hand

sides are polynomials it is very hard to tell if any nonsingular trajectories of the system are contained

in algebraic curves. We present an effective method of deciding, if a given system has an invariant

algebraic curve of a given degree. The method also allows the construction of examples of polynomial systems with invariant algebraic curves of a given degree. We present the first known example of degree 6 algebraic saddle-loop for polynomial system of degree 2 which has been found using the described method. We also present some new examples of invariant algebraic curves of degrees 4 and 5 with an interesting geometry.

By:* Grzegorz Swirszcz*

Published in: RC23120 in 2004

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