Abstract

We consider the polynomial vector fields of arbitrary degree in R-3 having the 2-dimensional algebraic torus T-2 (l, m, n) = {(x, y, z) is an element of R-3 : (x(2l) + y(2m) - r(2))(2) + z(2n) - 1 = 0}, where l, m, and n positive integers, and r is an element of (1, infinity), invariant by their flow. We study the possible configurations of invariant meridians and parallels that these vector fields can exhibit on T-2(l, m, n). Furthermore, we analyze when these invariant meridians or parallels are limit cycles.