Polynomial differential systems having a given Darbouxian first integral

Autor:	Llibre Saló, Jaume, Pantazi, Chara|||0000-0002-4394-404X
Jazyk:	angličtina
Rok vydání:	2004
Předmět:	Differential equations 34 Ordinary differential equations::34C Qualitative theory [Classificació AMS] First integral Equacions diferencials ordinàries Polynomial differential system Darbouxian function
Zdroj:	UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC)
Popis:	The Darbouxian theory of integrability allows to determine when a polynomial differential system in C2 has a first integral of the kind f λ1 1 ···f λp p exp(g/h) where fi , g and h are polynomials in C[x, y], and λi ∈ C for i = 1, . . . ,p. The functions of this form are called Darbouxian functions. Here, we solve the inverse problem, i.e. we characterize the polynomial vector fields in C2 having a given Darbouxian function as a first integral. On the other hand, using information about the degree of the invariant algebraic curves of a polynomial vector field, we improve the conditions for the existence of an integrating factor in the Darbouxian theory of integrability.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=RECOLECTA___::a511bba15fd37ff6ea8fc9da48657ded http://hdl.handle.net/2117/1212 Zobrazit plný text záznamu