Results 251 to 260 of about 398,271 (280)

PHASE PORTRAITS OF THE QUADRATIC SYSTEMS WITH A POLYNOMIAL INVERSE INTEGRATING FACTOR

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2009
We classify the phase portraits of all planar quadratic polynomial differential systems having a polynomial inverse integrating factor.
Antoni Ferragut, Jaume Llibre
exaly   +3 more sources

Non-formally integrable centers admitting an algebraic inverse integrating factor

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. Once the existence of an inverse integrat ing factor is established, we characterize the systems having a center. Among others, we characterize the centers
Cristóbal García
exaly   +6 more sources

Existence of inverse integrating factors and Lie symmetries for degenerate planar centers

Journal of Differential Equations, 2012
In this paper, the authors prove that every analytic planar vector field \(X\) with an isolated (possibly degenerate) center singularity at \(0\in\mathbb{R}^2\) admits a smooth inverse integrating factor (IIF) on a neighbourhood \(B\) of \(0\) that is positive in \(B-\{0\}\) and flat at the origin.
Jaume Gine, Daniel Peralta-Salas
exaly   +3 more sources

On the vanishing set of inverse integrating factors

Qualitative Theory of Dynamical Systems, 2000
An inverse integrating factor \(V\) (i.i.f. for short), associated to a \(C^1\) two-dimensional ordinary differential equation \(\dot x=P(x,y)\), \(\dot y=Q(x,y),\) is a \(C^1\) solution to the partial differential equation \(P {{\partial V}\over{\partial x}} +Q{ {\partial V}\over{\partial y}}= V \operatorname {div}(P,Q).\) Notice that if \(V\) and the
Berrone, Lucio R., Giacomini, Hector J.
openaire   +2 more sources

Generalized Hopf Bifurcation for Planar Vector Fields via the Inverse Integrating Factor [PDF]

Journal of Dynamics and Differential Equations, 2011
41 pages, no ...
Hector Giacomini, Maite Grau, Isaac A García   +2 more
exaly   +3 more sources

Polynomial inverse integrating factors for quadratic differential systems

Nonlinear Analysis: Theory, Methods & Applications, 2010
The authors consider the real planar quadratic polynomial system \[ \dot x = P(x,y), \quad \dot y = Q(x,y), \tag{1} \] where the dot denotes the derivative with respect to the time variable, and \(P,Q\) are quadratic polynomials. A function \(R(x,y)\) is called integrating factor of system (1), if \(R\) is a solution of the equation \(\text{div}(RP,RQ)
Coll, Bartomeu, Ferragut, Antoni, Llibre, Jaume   +2 more
openaire   +2 more sources

Photon output factor calculation from the inverse of the sector-integration equation

Medical Physics, 1999
A method to predict rectangular field output factors (OFs) of photon open beams for the Saturne 41 linear accelerator has been developed. The procedure is similar to the sector-integration method but the radiotherapy quantities corresponding to circular fields (circular functions) are calculated from one-dimensional OFs.
D E, Sanz, A L, Romaguera, N B, Acosta
openaire   +2 more sources

The inverse integrating factor for some classes of n-th order autonomous differential systems

Journal of Mathematical Analysis and Applications, 2015
Consider an \(n\)-order autonomous differential system \[ \dot{x}=p(x), \eqno{(1)} \] where \(x=(x_1,x_2,\ldots,x_n) \in D \subseteq \mathbb{R}^n\) and \(p(x)=(p_1(x),p_2(x),\ldots,p_n(x))\), with \(p_i\in C^1(D, \mathbb R)\) functions in \(D\). The vector field associated to system (1) is denoted by \[ \mathcal{X}= \sum_{i=1}^n p_i(x) \frac{\partial}{\
Hu, Yanxia, Chen, Yi
exaly   +2 more sources

Existence and nonexistence of Puiseux inverse integrating factors in analytic monodromic singularities

Studies in Applied Mathematics
AbstractIn this work, we present some criteria about the existence and nonexistence of both Puiseux inverse integrating factors and Puiseux first integrals for planar analytic vector fields having a monodromic singularity. These functions are a wide generalization of their formal or algebraic counterpart in Cartesian coordinates . We prove that none
Jaume Gine, Ana Livia Rodero, Isaac A García   +2 more
exaly   +3 more sources

One-parameter Lie groups and inverse integrating factors of n-th order autonomous systems

Journal of Mathematical Analysis and Applications, 2012
In the last years some works have appeared that show that the inverse integrating factors of a differential equations system can reveal some qualitative properties of the system. The key role that the inverse integrating factors play in the different theories of integrability has also been shown recently.
Hu, Yanxia, Xue, Chongzheng
exaly   +3 more sources