Results 11 to 20 of about 5,511,845 (178)
Non-existence of limit cycles via inverse integrating factors [PDF]
Electronic Journal of Differential Equations, 2011 It is known that if a planar differential systems has an inverse integrating factor, then all the limit cycles contained in the domain of definition of the inverse integrating factor are contained in the zero set of this function.
Leonardo Laura-Guarachi +2 more
doaj +4 more sources
Darboux integrability and the inverse integrating factor [PDF]
Journal of Differential Equations, 2003 We mainly study polynomial differential systems of the form dx/dt=P(x,y), dy/dt=Q(x,y), where P and Q are complex polynomials in the dependent complex variables x and y, and the independent variable t is either real or complex.
Giné, Jaume +3 more
core +3 more sources
The inverse integrating factor and the Poincaré map [PDF]
Transactions of the American Mathematical Society, 2010 27 pages, no figuresInternational audienceThis work is concerned with planar real analytic differential systems with an analytic inverse integrating factor defined in a neighborhood of a regular orbit.
Grau, Maite +2 more
core +3 more sources
The nondegenerate center problem and the inverse integrating factor [PDF]
Bulletin des Sciences Mathématiques, 2006 In this paper we study some aspects of the nondegenerate center problem for analytic and, in particular, for polynomial vector fields. The relation between the existence of an inverse integrating factor and the center problem is studied. The relationship
Giné, Jaume
core +2 more sources
Non-formally integrable centers admitting an algebraic inverse integrating factor [PDF]
Discrete and Continuous Dynamical Systems, 2018 Westudy the existence of a class of inverse integrating factor for a family of non formally integrable systems, in general, whose lowest-degree quasi-homogeneous term is a Hamiltonian vector field.
Garcia, C. +3 more
core +6 more sources
Nilpotent Systems Admitting an Algebraic Inverse Integrating Factor over C((x,y)) [PDF]
Qualitative Theory of Dynamical Systems, 2011 We characterize the nilpotent systems whose lowest degree quasihomogeneous term is (y, σ xn)T, σ = ±1, which have an algebraic inverse integrating factor over C((x,y)) .
Reyes Columé, Manuel +2 more
core +6 more sources
Integrable systems via polynomial inverse integrating factors [PDF]
Bulletin des Sciences Mathématiques, 2002 We study the integrability of two-dimensional autonomous systems in the plane of the form ẋ=−y+Xs(x,y),ẏ=x+Ys(x,y), where Xs(x,y) and Ys(x,y) are homogeneous polynomials of degree s with s⩾2.
Grau, M., Chavarriga, J., Giné, J.
core +2 more sources
Linearizable planar differential systems via the inverse integrating factor
Journal of Physics A: Mathematical and Theoretical, 2008 International audienceOur purpose in this paper is to study when a planar differential system polynomial in one variable linearizes in the sense that it has an inverse integrating factor which can be constructed by means of the solutions of linear ...
Giné, Jaume +2 more
core +3 more sources
On the Vanishing Set of Inverse Integrating Factors
Qualitative Theory of Dynamical Systems, 2000 We study in this paper $\mathcal{C}^{1}$ two-dimensional dynamical systems of the form $\; \stackrel{.}{x} = P(x,y),\; \;\stackrel{.}{y} = Q(x,y).$ We analyse the properties of the vanishing set of inverse integrating factors V, which are defined as ...
Berrone, Lucio R., Giacomini, Hector J.
core +3 more sources
Center problem with characteristic directions and inverse integrating factors [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2022 We consider the center-focus problem for analytic families of planar vector fields having a monodromic singularity with characteristic directions. We give a method to compute the center conditions of the family provided there is an inverse integrating factor whose expression in polar coordinates has the exceptional divisor of the first polar blow-up as
Isaac A. García, Jaume Giné
openaire +2 more sources