Quantitative theory of ordinary differential equations and tangential Hilbert 16th problem

Details Quantitative theory of ordinary differential equations and tangential Hilbert 16th problem Quantitative theory of ordinary differential equations and tangential Hilbert 16th problem

2001-04-12

arxiv.org/abs/math/0104140v3

MR2180125 (2006g:34062) On finiteness in differential equations and Diophantine geometry, 41--109, CRM Monogr. Ser., 24, Amer.

Mathematics

Dynamical Systems

Expanded lecture notes of the course delivered on the Workshop "Asymptotic series, differential algebra and finiteness theorem

Scientific paper

These highly informal lecture notes aim at introducing and explaining several closely related problems on zeros of analytic functions defined by ordinary differential equations and systems of such equations. The main incentive for this study was its potential application to the tangential Hilbert 16th problem on zeros of complete Abelian integrals. The exposition consists mostly of examples illustrating various phenomena related to this problem. Sometimes these examples give an insight concerning the proofs, though the complete exposition of the latter is mostly relegated to separate expositions. For related and quoted articles, check the author's homepage http://www.wisdom.weizmann.ac.il/~yakov .

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