The Poincaré Problem, algebraic integrability and dicritical divisors

Details The Poincaré Problem, algebraic integrability and dicritical divisors The Poincaré Problem, algebraic integrability and dicritical divisors

2011-10-13

arxiv.org/abs/1110.2973v1

Mathematics

Dynamical Systems

Scientific paper

We solve the Poincar\'e problem for plane foliations with only one dicritical divisor. Moreover, in this case, we give an algorithm that decides whether a foliation has a rational first integral and computes it in the affirmative case. We also provide an algorithm to compute a rational first integral of prefixed genus $g\neq 1$ of any type of plane foliation $\cf$. When the number of dicritical divisors dic$(\cf)$ is larger than two, this algorithm depends on suitable families of invariant curves. When dic$(\cf) = 2$, it proves that the degree of the rational first integral can be bounded only in terms of $g$, the degree of $\cf$ and the local analytic type of the dicritical singularities of $\cf$.

Affiliated with

Also associated with

No associations

Rating

The Poincaré Problem, algebraic integrability and dicritical divisors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Poincaré Problem, algebraic integrability and dicritical divisors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Poincaré Problem, algebraic integrability and dicritical divisors will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-500524