Hilbert’s 16th Problem and Its Weak Form
Part of the Advanced Courses in Mathematics CRM Barcelona book series (ACMBIRK)
Consider the planar differential systems
where Pn and Qn 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 ):
$$ \dot x = P_n (x,y),\dot y = Q_n (x,y), $$
For a given integer n, what is the maximum number of limit cycles of system (1.1) for all possible Pn and Qn ? And how about the possible relative positions of the limit cycles ?
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© Birkhäuser Verlag 2007