sequences from Hilbert's 16th problem?
N. J. A. Sloane
njas at research.att.com
Sat Apr 9 17:57:02 CEST 2005
Dear Math-Fun and Seqfans,
In his 2002 survey,
MR1898209 (2003c:34001) Ilyashenko, Yu. Centennial history of Hilbert's 16th problem. Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 3, 301--354 (electronic). (Reviewer: Lubomir Gavrilov) 34-02 (34C07 37C10 37F75)
the author mentions that Petrovskii and Landis gave an incorrect proof that
the Hilbert number H(n) is bounded above by P_3(n), "a certain polynomial
of degree 3 [in n]". The reference is to:
MR0073004 (17,364d)
Petrovski\u\i, I. G.; Landis, E. M.
On the number of limit cycles of the equation $dy/dx=P(x,y)/Q(x,y)$, where $P$ and $Q$ are polynomials of 2nd degree. (Russian)
Mat. Sb. N.S. 37(79) (1955), 209--250.
My question is, what is this sequence P_3(n) ?
Later in the article Ilyashenko mentions a second Hilbert-type
sequence E(n) (on page 305). Same question.
NJAS
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