[图书][B] Integrability of dynamical systems: algebra and analysis
X Zhang - 2017 - Springer
The theory of integrability plays an important role in the study of the dynamics of differential
systems. This theory is related to several branches of mathematics, such as algebraic …
systems. This theory is related to several branches of mathematics, such as algebraic …
On the Darboux integrability of polynomial differential systems
J Llibre, X Zhang - Qualitative theory of dynamical systems, 2012 - Springer
On the Darboux Integrability of Polynomial Differential Systems Page 1 Qual. Theory Dyn. Syst.
(2012) 11:129–144 DOI 10.1007/s12346-011-0053-x Qualitative Theory of Dynamical Systems …
(2012) 11:129–144 DOI 10.1007/s12346-011-0053-x Qualitative Theory of Dynamical Systems …
A survey on the inverse integrating factor
IA García, M Grau - Qualitative Theory of Dynamical Systems, 2010 - Springer
The relation between limit cycles of planar differential systems and the inverse integrating
factor was first shown in an article of Giacomini, Llibre and Viano appeared in 1996. From …
factor was first shown in an article of Giacomini, Llibre and Viano appeared in 1996. From …
Existence of an inverse integrating factor, center problem and integrability of a class of nilpotent systems
We characterize the nilpotent systems whose lowest degree quasi-homogeneous term is (y,
σxn) T, σ=±1, having a formal inverse integrating factor. We prove that, for n even, the …
σxn) T, σ=±1, having a formal inverse integrating factor. We prove that, for n even, the …
[HTML][HTML] Reduction of integrable planar polynomial differential systems
J Gine - Applied Mathematics Letters, 2012 - Elsevier
The integrability problem consists in finding the class of functions, a first integral of a given
planar polynomial differential system must belong to. We recall the characterization of …
planar polynomial differential system must belong to. We recall the characterization of …
Phase Portraits of the Quadratic Systems with a Polynomial Inverse Integrating Factor.
PHASE PORTRAITS OF THE QUADRATIC SYSTEMS WITH A POLYNOMIAL INVERSE
INTEGRATING FACTOR Page 1 April 23, 2009 10:1 02329 Tutorials and Reviews International …
INTEGRATING FACTOR Page 1 April 23, 2009 10:1 02329 Tutorials and Reviews International …
On the remarkable values of the rational first integrals of polynomial vector fields
A Ferragut, J Llibre - Journal of Differential Equations, 2007 - Elsevier
The remarkable values for polynomial vector fields in the plane having a rational first integral
were introduced by Poincaré. He was mainly interested in their algebraic aspects. Here we …
were introduced by Poincaré. He was mainly interested in their algebraic aspects. Here we …
The completely integrable differential systems are essentially linear differential systems
Let ̇ x= f (x) x˙= f (x) be a C^ k C k autonomous differential system with k ∈ N ∪ {∞, ω\} k∈
N∪∞, ω defined in an open subset\varOmega Ω of R^ n R n. Assume that the system ̇ x= f …
N∪∞, ω defined in an open subset\varOmega Ω of R^ n R n. Assume that the system ̇ x= f …
A hybrid symbolic-numerical approach to the center-focus problem
We propose a new hybrid symbolic-numerical approach to the center-focus problem. The
method allowed us to obtain center conditions for a three-dimensional system of differential …
method allowed us to obtain center conditions for a three-dimensional system of differential …
Center problem for third-order ODEs
A Mahdi - International Journal of Bifurcation and Chaos, 2013 - World Scientific
CENTER PROBLEM FOR THIRD-ORDER ODEs Page 1 May 27, 2013 20:29 WSPC/S0218-1274
1350078 Papers International Journal of Bifurcation and Chaos, Vol. 23, No. 5 (2013) 1350078 …
1350078 Papers International Journal of Bifurcation and Chaos, Vol. 23, No. 5 (2013) 1350078 …