Results 11 to 20 of about 131,499 (275)
Liouvillian First Integrals for Generalized Liénard Polynomial Differential Systems [PDF]
Advanced Nonlinear Studies, 2013 Abstract We study the Liouvillian first integrals for the generalized Liénard polynomial differential systems of the form xʹ = y, yʹ = -g(x) - f(x)y, where g(x) and f(x) are arbitrary polynomials such that 2 ≤ deg g ≤ deg f.
Jaume Llibre, Clàudia Valls
exaly +8 more sources
Liouvillian First Integrals for Generalized Riccati Polynomial Differential Systems [PDF]
Advanced Nonlinear Studies, 2015 Abstract We study the existence and non-existence of Liouvillian first integrals for the generalized Riccati polynomial differential systems of the form xʹ = y, yʹ = a(x)y2 +b(x)y+c(x), where a(x), b(x) and c(x) are polynomials.
Llibre, Jaume, Valls, Clàudia
exaly +7 more sources
The Kepler Problem: Polynomial Algebra of Nonpolynomial First Integrals [PDF]
Regular and Chaotic Dynamics, 2019 LaTex with AMS fonts, 18 ...
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Polynomial first integrals of quadratic vector fields
Journal of Differential Equations, 2006 The goal of this paper is to characterize those quadratic differential equations in the plane having a polynomial first integral, and to provide an explicit expression of these systems as well as of their polynomial first integrals. It is well known that if the system writes as \[ \dot x=P(x,y), \quad \dot y=Q(x,y) \] it is not restrictive to assume ...
Chavarriga, Javier +4 more
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On planar polynomial vector fields with elementary first integrals [PDF]
Journal of Differential Equations, 2019 We show that under rather general conditions a polynomial differential system having an elementary first integral already must admit a Darboux first integral, and we explicitly characterize the vector fields in this class. We also investigate some exceptional cases, i.e. equations admitting an elementary first integral but not a Darboux first integral.
Colin Christopher +3 more
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Darboux Integrability of a Generalized 3D Chaotic Sprott ET9 System
مجلة بغداد للعلوم, 2022 In this paper, the first integrals of Darboux type of the generalized Sprott ET9 chaotic system will be studied. This study showed that the system has no polynomial, rational, analytic and Darboux first integrals for any value of .
Adnan Ali Jalal +2 more
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Anais da Academia Brasileira de Ciências, 2021 Poincaré in 1891 asked about the necessary and sufficient conditions in order to characterize when a polynomial differential system in the plane has a rational first integral. Here we solve this question for the class of Liénard differential equations
JAUME LLIBRE +2 more
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On the polynomial differential systems having polynomial first integrals
Bulletin des Sciences Mathématiques, 2012 We consider the class of complex planar polynomial differential systems having a polynomial first integral. Inside this class the systems having minimal polynomial first integrals without critical remarkable values are the Hamiltonian ones. Here we mainly study the subclass of polynomial differential systems such that their minimal polynomial first ...
García, Belen +2 more
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Reduction of Feynman integrals in the parametric representation II: reduction of tensor integrals
European Physical Journal C: Particles and Fields, 2021 In a recent paper by the author (Chen in JHEP 02:115, 2020), the reduction of Feynman integrals in the parametric representation was considered. Tensor integrals were directly parametrized by using a generator method.
Wen Chen
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Darboux integrability of a hyperjerk memristive system
Zanco Journal of Pure and Applied Sciences, 2023 In this work, we investigate the following novel four-dimensional dynamical memristive system (see, (Prousalis et al., 2017)) This system, in a certain area of the parameter space, exhibits hyper-jerk dynamics and a line of singularities passing ...
Niazy Hady Hussein ,Soran Mohammed Khudur
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