M. Tismenetsky
International Journal of Computer Mathematics
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 whether 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 a 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. © World Scientific Publishing Company.
M. Tismenetsky
International Journal of Computer Mathematics
Michael Ray, Yves C. Martin
Proceedings of SPIE - The International Society for Optical Engineering
Peter Wendt
Electronic Imaging: Advanced Devices and Systems 1990
R.A. Brualdi, A.J. Hoffman
Linear Algebra and Its Applications