Geodesic
Polynomial Dynamical Systems and Ordinary Differential Equations Associated with the Heat Equation
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 3, pp. 16-37

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: polynomial dynamical systems, heat equation, Chazy equation, Darboux–Halphen system. 
@article{FAA_2012_46_3_a1,
     author = {E. Yu. Bunkova and V. M. Buchstaber},
     title = {Polynomial {Dynamical} {Systems} and {Ordinary} {Differential} {Equations} {Associated} with the {Heat} {Equation}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {16--37},
     publisher = {mathdoc},
     volume = {46},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2012_46_3_a1/}
}
TY  - JOUR
AU  - E. Yu. Bunkova
AU  - V. M. Buchstaber
TI  - Polynomial Dynamical Systems and Ordinary Differential Equations Associated with the Heat Equation
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2012
SP  - 16
EP  - 37
VL  - 46
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2012_46_3_a1/
LA  - ru
ID  - FAA_2012_46_3_a1
ER  - 
%0 Journal Article
%A E. Yu. Bunkova
%A V. M. Buchstaber
%T Polynomial Dynamical Systems and Ordinary Differential Equations Associated with the Heat Equation
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2012
%P 16-37
%V 46
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2012_46_3_a1/
%G ru
%F FAA_2012_46_3_a1
E. Yu. Bunkova; V. M. Buchstaber. Polynomial Dynamical Systems and Ordinary Differential Equations Associated with the Heat Equation. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 3, pp. 16-37. http://geodesic.mathdoc.fr/item/FAA_2012_46_3_a1/