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International Workshop «Geometric Structures in Integrable Systems»
October 30, 2012 14:00, Moscow, M.V. Lomonosov Moscow State University
 


Introducing a new notion of algebraic integrability.

E. Yu. Bunkova, V. M. Buchstaber

Steklov Mathematical Institute of the Russian Academy of Sciences
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Flash Video 228.7 Mb
MP4 228.7 Mb
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Adobe PDF 294.9 Kb

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E. Yu. Bunkova, V. M. Buchstaber


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Abstract: Let us consider the general homogeneous quadratic dynamic system. We will call it algebraically integrable by given functions $h_{1},…,h_{n}$ if the set of roots of the equation $\xi ^{n}-h_{1}\xi ^{n-1}+…+(-1)^{n}h_{n}\equiv 0$ solves the dynamic system.
The talk introduces this new notion of algebraic integrability and presents a wide class of quadratic dynamic systems that are algebraically integrable by the set of functions $h_{1},…,h_{n}$ where $h_{1}$ is the solution to an ordinary differential equation of order $n$ and $h_{k}$ are differential polynomials in $h_{1}$, $k=2,…,n$. Results on algebraically integrable quadratic dynamic systems and non-linear ordinary differential equations related to them are obtained. Classical examples like the Darboux–Halphen system are considered.

Materials: gsis_ebounkova.pdf (294.9 Kb)

Language: English

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