AbstractEliminating the arbitrary coefficients in the equation of a generic plane curve of order n by computing sufficiently many derivatives, one obtains a differential equation. This is a projective invariant. The first one, corresponding to conics, has been obtained by Monge. Sylvester, Halphen, Cartan used invariants of higher order. The expression of these invariants is rather complicated, but becomes much simpler when interpreted in terms of symmetric functions
In this paper we address the Poincare problem, on plane polynomial vector fields, under some conditi...
In this paper we address the Poincaré problem, on plane polynomial vector fields, under some conditi...
In the framework of the projective geometric theory of systems of differential equations, which is b...
Eliminating the arbitrary coefficients in the equation of a generic plane curve of order $n$ by comp...
We consider a plane polynomial vector field $P(x,y)dx+Q(x,y)dy$ of degree $m>1$. To each algebraic i...
Algebra of projective differential invariants and description of projective classes of regular smoot...
The geometric approach to the study of differential equations goes back to Sophus Lie and Elie Carta...
Agraïments: The second author is supported by CNPq-Brazil grant 308315/2012-0 and by FAPESP grant 12...
A pure algebraic approach to differential invariants of curves and surfaces is presented. By the use...
A conic section is a plane quadratic curve, that is, the graph of an equation of the form ax² + bxy ...
We propose definitions of homogeneity and projective equivalence for systems of ordinary differentia...
The notion of strict equivalence for order one differential equations of the form f(y′,y,z)=0 with c...
We classify the phase portraits of quadratic polynomial differential systems having some relevant cl...
The theory of generic smooth closed plane curves initiated by Vladimir Arnold is a beautiful fusion ...
Abstract. An invariant solution of a differential equation is a solution of the differential equatio...
In this paper we address the Poincare problem, on plane polynomial vector fields, under some conditi...
In this paper we address the Poincaré problem, on plane polynomial vector fields, under some conditi...
In the framework of the projective geometric theory of systems of differential equations, which is b...
Eliminating the arbitrary coefficients in the equation of a generic plane curve of order $n$ by comp...
We consider a plane polynomial vector field $P(x,y)dx+Q(x,y)dy$ of degree $m>1$. To each algebraic i...
Algebra of projective differential invariants and description of projective classes of regular smoot...
The geometric approach to the study of differential equations goes back to Sophus Lie and Elie Carta...
Agraïments: The second author is supported by CNPq-Brazil grant 308315/2012-0 and by FAPESP grant 12...
A pure algebraic approach to differential invariants of curves and surfaces is presented. By the use...
A conic section is a plane quadratic curve, that is, the graph of an equation of the form ax² + bxy ...
We propose definitions of homogeneity and projective equivalence for systems of ordinary differentia...
The notion of strict equivalence for order one differential equations of the form f(y′,y,z)=0 with c...
We classify the phase portraits of quadratic polynomial differential systems having some relevant cl...
The theory of generic smooth closed plane curves initiated by Vladimir Arnold is a beautiful fusion ...
Abstract. An invariant solution of a differential equation is a solution of the differential equatio...
In this paper we address the Poincare problem, on plane polynomial vector fields, under some conditi...
In this paper we address the Poincaré problem, on plane polynomial vector fields, under some conditi...
In the framework of the projective geometric theory of systems of differential equations, which is b...
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