Polynomial dynamical systems and ordinary differential equations associated with the heat equation
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We consider homogeneous polynomial dynamical systems in n-space. To any such system our construction matches a nonlinear ordinary differential equation and an algorithm for constructing a solution of the heat equation. The classical solution given by the Gaussian function corresponds to the case n = 0, while solutions defined by the elliptic theta-function lead to the Chazy-3 equation and correspond to the case n = 2. We explicitly describe the family of ordinary differential equations arising in our approach and its relationship with the wide-known Darboux-Halphen quadratic dynamical systems and their generalizations.
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- Polynomial dynamical systems and ordinary differential equations associated with the heat equation
Functional Analysis and Its Applications
Volume 46, Issue 3 , pp 173-190
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- SP MAIK Nauka/Interperiodica
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- polynomial dynamical systems
- heat equation
- Chazy equation
- Darboux-Halphen system