Around Hilbert-Arnold Problem

Vadim Kaloshin

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Around Hilbert-Arnold Problem

Vadim Kaloshin

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Abstract

This lectures notes consists of four lectures. The first lecture discusses questions around Hilbert-Arnold Problem which is naturally arises from Quantitative Hilbert 16-th problem. In the second lecture we outline author's solution of a weak form of Local Hilbert-Arnold Problem. This solution provides an independent proof of Ilyashenko-Yakovenko Finiteness Theorem. The third lecture discusses question of existence of a_P-stratification of Thom and presents a simple geometric proof of existence of such a stratification for polynomial functions, which was originally proven by Hironaka. The forth lecture gives application of Grigoriev-Yakovenko's construction to the problem of growth of the number of periodic points and the problem of bifurcation of spacial polycycles. The latter problem naturally generalizes Local Hilbert-Arnold Problem.

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BibTeX RIS

Vadim Kaloshin. 2001-11-06. Around Hilbert-Arnold Problem. https://arxiv.org/abs/math/0111053

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