The conic h(x, y) = [x.sup.2] + [cy.sup.2] -1 = 0, c [member of] R, is an invariant
algebraic curve of system (1).
If a(S) = 1, there is an algebraic reduction of S, a fibration [PI] : S [right arrow] B such that B is an
algebraic curve and such that any meromorphic function on S is the pullback by n of an algebraic function on B.
Under this mapping, a ruling of a regulus corresponds to an
algebraic curve in [R.sup.4].
The condition that an
algebraic curve is invariant is in particular a condition of tangency, i.e.
As singular points of an
algebraic curve are the solutions of a polynomial system, most of algorithms in [10-15] solve the polynomial system either by Grobner basis method described in [16] or by resultant computation.
Teillaud, "The offset to an
algebraic curve and an application to conics," in Proceedings of the International Conference on Computational Science and Its Applications (ICCSA '05), pp.
Mikhalkin [Mik05, Theorem 1] one can replace the
algebraic curve count in [CP.sup.2] by an enumeration of certain tropical curves.
We study the local dynamics of maps f(z) = - z - [[SIGMA].sup.[infinity].sub.n=1] [alpha]n [z.sup.n+1], where f (z) is an irreducible branch of the
algebraic curveIn this paper, I investigate the
algebraic curve defined by the relation