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Let C(t) : I 7! R2 be a simple closed unit-speed C2 curve in R2 with normal ~n(t). The
curve C generates a distribution ¡ which acts on vector ˉelds ~v(x1; x2) : R2 7! R2 by line
integration ac...
Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time
Darboux polynomials rational first integrals bounded degree
2010/12/7
In this paper we study planar polynomial differential systems of this form: dX dt = ˙X = A(X, Y ),dY dt = ˙Y = B(X, Y ),where A,B ∈ Z[X, Y ] and deg A ≤ d, degB ≤ d, kAk1 ≤ H and kBk1 ≤H. A lot of pro...