Results 21 to 30 of about 262,161 (280)
Strongly formal Weierstrass non-integrability for polynomial differential systems in $\mathbb{C}^2$
Electronic Journal of Qualitative Theory of Differential Equations, 2020 Recently it has been given a criterion for determining the weakly formal Weierstrass non-integrability of polynomial differential systems in $\mathbb{C}^2$.
Jaume Giné, Jaume Llibre
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Acta et Commentationes: Ştiinţe Exacte şi ale Naturii, 2023 The present study delves into the investigation of phase portraits of polynomial differential systems, which are systems of differential equations of the form $\frac{dx}{dt} = P(x,y), \frac{dy}{dt} = Q(x,y)$, where $x$ and $y$ are the dependent ...
Vadim Repeșco
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Integrable differential systems for deformed Laguerre–Hahn orthogonal polynomials
Nonlinearity, 2023 AbstractOur work studies sequences of orthogonal polynomials{Pn(x)}n⩾0of the Laguerre–Hahn class, whose Stieltjes functions satisfy a Riccati type differential equation with polynomial coefficients, which are subject to a deformation parametert. We derive systems of differential equations and give Lax pairs, yielding nonlinear differential equations ...
Maria das Neves Rebocho, Nicholas Witte
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The Stability Interval of the Set of Linear System [PDF]
International Journal of Electronics and Telecommunications, 2021 The article considers the problem of stability of interval-defined linear systems based on the Hurwitz and Lienard- Shipar interval criteria. Krylov, Leverier, and Leverier- Danilevsky algorithms are implemented for automated construction and analysis of
Talgat Mazakov +5 more
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On the Darboux Integrability of Polynomial Differential Systems [PDF]
Qualitative Theory of Dynamical Systems, 2011 A method to find explicit closed forms for a first integral of a planar polynomial differential system from its invariant algebraic curves was given by \textit{G. Darboux} [C. R. LXXXVI, 581--586 (1878; JFM 10.0214.03)]. From that moment on, many research articles were devoted to the study of the integrability problem by using the invariant algebraic ...
Llibre, Jaume, Zhang, Xiang
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Phase Portraits of Families VII and VIII of the Quadratic Systems
Axioms, 2023 The quadratic polynomial differential systems in a plane are the easiest nonlinear differential systems. They have been studied intensively due to their nonlinearity and the large number of applications.
Laurent Cairó, Jaume Llibre
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Maximum number of limit cycles for generalized Liénard polynomial differential systems [PDF]
Mathematica Bohemica, 2021 We consider limit cycles of a class of polynomial differential systems of the form \begin{cases} \dot{x}=y, \dot{y}=-x-\varepsilon(g_{21}( x) y^{2\alpha+1} +f_{21}(x) y^{2\beta})-\varepsilon^2(g_{22}( x) y^{2\alpha+1}+f_{22}( x) y^{2\beta}), \end ...
Aziza Berbache +2 more
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Duality, Biorthogonal Polynomials and Multi-Matrix Models [PDF]
, 2001 The statistical distribution of eigenvalues of pairs of coupled random matrices can be expressed in terms of integral kernels having a generalized Christoffel--Darboux form constructed from sequences of biorthogonal polynomials.
Bertola, M., Eynard, B., Harnad, J.
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Analytic integrability of quadratic–linear polynomial differential systems [PDF]
Ergodic Theory and Dynamical Systems, 2009 AbstractFor the quadratic–linear polynomial differential systems with a finite singular point, we classify the ones which have a global analytic first integral, and provide the explicit expression of their first integrals.
Llibre, Jaume, Valls, Clàudia
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Electronic Journal of Qualitative Theory of Differential Equations, 2015 We study the existence and non--existence of periodic orbits and limit cycles for planar polynomial differential systems of degree $n$ having $n$ real invariant straight lines taking into account their multiplicities.
Jaume Llibre, Ana Rodrigues
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