On local description of two-dimensional geodesic flows with a polynomial first integral [PDF]
, 2015 In this paper we present a construction of multiparametric families of two-dimensional metrics with a polynomial first integral of arbitrary degree in momenta.
M. Pavlov, S. P. Tsarev
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Darboux and rational first integrals for a family of cubic three dimensional systems
Zanco Journal of Pure and Applied Sciences, 2021 In this paper, we investigate the first integrals of the following system exam.PNG exam1.PNG This kind of system is a particular case of the jerk cubic three dimensional polynomial differential systems.
Sarbast Hussein Mikaeel, Azad I. Amen
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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
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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
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An Efficient Collocation Method for the Numerical Solutions of the Pantograph-Type Volterra Hammerstein Integral Equations and its Convergence Analysis [PDF]
Computational Algorithms and Numerical Dimensions, 2022 In this work, we consider a collocation method for solving the pantograph-type Volterra Hammerstein integral equations based on the first kind Chebyshev polynomials. We use the Lagrange interpolating polynomial to approximate the solution.
Hashem Saberi Najafi +2 more
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Explicit Construction of First Integrals with Quasi-monomial Terms from the Painlev\'{e} Series [PDF]
, 2004 The Painlev\'{e} and weak Painlev\'{e} conjectures have been used widely to identify new integrable nonlinear dynamical systems. For a system which passes the Painlev\'{e} test, the calculation of the integrals relies on a variety of methods which are ...
Bountis, Tassos +2 more
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Sharp estimates for oscillatory integral operators via polynomial partitioning [PDF]
Acta Mathematica, 2017 The sharp range of $L^p$-estimates for the class of H\"ormander-type oscillatory integral operators is established in all dimensions under a positive-definite assumption on the phase. This is achieved by generalising a recent approach of the first author
L. Guth, J. Hickman, M. Iliopoulou
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Polynomial First Integrals of Quadratic Systems
Rocky Mountain Journal of Mathematics, 2001 The paper contains a classification and the topological phase portraits of all quadratic systems having minimal polynomial first integrals of degree at most 4. The authors prove the existence of minimal polynomial first integrals of any degree for quadratic systems and show that such systems having more than three invariant straight lines have no ...
Llibre, Jaume, Zhang, Xiang
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Science Journal of University of Zakho, 2017 The main purpose of this paper is to study the existence of polynomial inverse integrating factor and first integral, and non-existence of limit cycles for all systems. Furthermore, we consider some applications.
Ahmed M. Hussien
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Computer studies of polynomial solutions for gyrostat dynamics [PDF]
Компьютерные исследования и моделирование, 2018 We study polynomial solutions of gyrostat motion equations under potential and gyroscopic forces applied and of gyrostat motion equations in magnetic field taking into account Barnett-London effect.
Alexander Vasilievich Zyza
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