2007 | OriginalPaper | Chapter
Hilbert’s 16th Problem and Its Weak Form
Published in: Limit Cycles of Differential Equations
Publisher: Birkhäuser Basel
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
Consider the planar differential systems
(1.1)
$$ \dot x = P_n (x,y),\dot y = Q_n (x,y), $$
where
P
n
and
Q
n
are real polynomials in
x, y
and the maximum degree of
P
and
Q
is
n
. The second half of the famous Hilbert’s 16th problem, proposed in 1900, can be stated as follows (see [70]):
For a given integer n, what is the maximum number of limit cycles of system
(1.1)
for all possible P
n
and Q
n
? And how about the possible relative positions of the limit cycles ?