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SUMMARY:Maria Demina (National Research University Higher School of Econom
 ics\, Russia)
DTSTART:20210216T140000Z
DTEND:20210216T150000Z
DTSTAMP:20260422T201404Z
UID:CAvid/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/30/">A
 lgebraic invariants\, integrability\, and meromorphic solutions</a>\nby Ma
 ria Demina (National Research University Higher School of Economics\, Russ
 ia) as part of CAvid: Complex Analysis video seminar\n\nLecture held in N/
 A.\n\nAbstract\nConsider an autonomous algebraic ordinary differential equ
 ation of order higher than one. The aim of the talk is to address the foll
 owing questions.\n\n1. Does there exist an autonomous algebraic first-orde
 r ordinary differential equation compatible with the original equation?\n\
 n2. If yes\, how to find all such equations?\n \n\nBivariate polynomials p
 roducing autonomous algebraic first-order ordinary differential equations 
 compatible with the equation under consideration are called algebraic inva
 riants. The main difficulty in deriving irreducible algebraic invariants l
 ies in the fact that the degrees of related bivariate polynomials are not 
 known in advance.\n\nAlgebraic invariants are important from theoretical a
 nd practical point of views. In the two-dimensional case algebraic invaria
 nts are key objects in establishing Darboux and Liouvillian integrability 
 of the original ordinary differential equation. In addition\, algebraic in
 variants can be used to perform the classification of W-meromorphic soluti
 ons of ordinary differential equations. We shall pay some attention to the
 se applications.\n
LOCATION:https://researchseminars.org/talk/CAvid/30/
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