Polynomial algebra of constants of the Lotka-Volterra system
Moulin Ollagnier, Jean ; Nowicki, Andrzej
Colloquium Mathematicae, Tome 79 (1999), p. 263-270 / Harvested from The Polish Digital Mathematics Library
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Let k be a field of characteristic zero. We describe the kernel of any quadratic homogeneous derivation d:k[x,y,z] → k[x,y,z] of the form d=x(Cy+z)∂∂x+y(Az+x)∂∂y+z(Bx+y)∂∂z, called the Lotka-Volterra derivation, where A,B,C ∈ k.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:210738 
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     author = {Jean Moulin Ollagnier and Andrzej Nowicki},
     title = {Polynomial algebra of constants of the Lotka-Volterra system},
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     volume = {79},
     year = {1999},
     pages = {263-270},
     zbl = {1004.12004},
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Moulin Ollagnier, Jean; Nowicki, Andrzej. Polynomial algebra of constants of the Lotka-Volterra system. Colloquium Mathematicae, Tome 79 (1999) pp. 263-270. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv81i2p263bwm/

[000] [1] B. Grammaticos, J. Moulin Ollagnier, A. Ramani, J.-M. Strelcyn and S. Wojciechowski, Integrals of quadratic ordinary differential equations in ℝ3: the Lotka-Volterra system, Phys. A 163 (1990), 683-722. | Zbl 0714.34005

[001] [2] J. Moulin Ollagnier, Polynomial first integrals of the Lotka-Volterra system, Bull. Sci. Math. 121 (1997), 463-476. | Zbl 0887.34002

[002] [3] J. Moulin Ollagnier, Rational integration of the Lotka-Volterra system, ibid. 123 (1999), 437-466.

[003] [4] J. Moulin Ollagnier, A. Nowicki and J.-M. Strelcyn, On the non-existence of constants of derivations: the proof of a theorem of Jouanolou and its development, ibid. 119 (1995), 195-233. | Zbl 0855.34010

[004] [5] A. Nowicki, Polynomial derivations and their rings of constants, N. Copernicus University Press, Toruń, 1994.

[005] [6] A. Nowicki, On the non-existence of rational first integrals for systems of linear differential equations, Linear Algebra Appl. 235 (1996), 107-120. | Zbl 0843.34013

[006] [7] A. Nowicki and M. Nagata, Rings of constants for k-derivations in k[x1,...,xn], J. Math. Kyoto Univ. 28 (1988), 111-118. | Zbl 0665.12024

[007] [8] A. Nowicki and J.-M. Strelcyn, Generators of rings of constants for some diagonal derivations in polynomial rings, J. Pure Appl. Algebra 101 (1995), 207-212. | Zbl 0832.12002