William Hinsberg, Joy Cheng, et al.
SPIE Advanced Lithography 2010
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.
William Hinsberg, Joy Cheng, et al.
SPIE Advanced Lithography 2010
S.F. Fan, W.B. Yun, et al.
Proceedings of SPIE 1989
Kafai Lai, Alan E. Rosenbluth, et al.
SPIE Advanced Lithography 2007
F. Odeh, I. Tadjbakhsh
Archive for Rational Mechanics and Analysis