Variation of argument and Bernstein index for holomorphic functions on Riemann surfaces
| dc.creator | Ilyashenko, Yulij | |
| dc.date | 2006-01-03 | |
| dc.date.accessioned | 2026-07-07T06:58:29Z | |
| dc.date.available | 2026-07-07T06:58:29Z | |
| dc.description | An upper bound of the variation of argument of a holomorphic function along a curve on a Riemann surface is given. This bound is expressed through the Bernstein index of the function multiplied by a geometric constant. The Bernstein index characterizes growth of the function from a smaller domain to a larger one. The geometric constant in the estimate is explicitly given. This result is applied in \cite {GI} to the solution of the restricted version of the infinitesimal Hilbert 16th problem, namely, to upper estimates of the number of zeros of abelian integrals in complex domains. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0601043 | |
| dc.identifier | http://arxiv.org/abs/math/0601043 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107374 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 58F21 | |
| dc.title | Variation of argument and Bernstein index for holomorphic functions on Riemann surfaces | |
| dc.type | text |