The variational principle
Sur quelques classes d’applications de dans les ensembles finis
Liouvillian first integrals of homogeneouspolynomial 3-dimensional vector fields
Given a 3-dimensional vector field V with coordinates , and that are homogeneous polynomials in the ring k[x,y,z], we give a necessary and sufficient condition for the existence of a Liouvillian first integral of V which is homogeneous of degree 0. This condition is the existence of some 1-forms with coordinates in the ring k[x,y,z] enjoying precise properties; in particular, they have to be integrable in the sense of Pfaff and orthogonal to the vector field V. Thus, our theorem links the existence...
Théorème ergodique presque sous-additif et convergence en moyenne de l'information
Filtre moyennant et valeurs moyennes des capacités invariantes
Systèmes dynamiques topologiques I. Étude des limites de cobords
Polynomial algebra of constants of the Lotka-Volterra system
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 , called the Lotka-Volterra derivation, where A,B,C ∈ k.
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