Around Hilbert –Arnol′d Problem
نویسنده
چکیده
H(n) = uniform bound for the number of limit cycles of (1) . One way to formulate the Hilbert 16th problem is the following: Hilbert 16th Problem (HP). Estimate H(n) for any n ∈ Z+. To prove that H(1) = 0 is an exercise, but to find H(2) is already a difficult unsolved problem (see [DRR,DMR] for work in this direction). Below we discuss two of the most significant branches of research HP has generated: existential and tangential Hilbert 16th problems. 1.1.1. The tangential Hilbert 16th problem. Consider a polynomial perturbation of a Hamiltonian polynomial line field
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