Results 21 to 30 of about 131,499 (275)
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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Polynomial first integrals for weight-homogeneous planar polynomial differential systems of weight degree~$4$ [PDF]
Rocky Mountain Journal of Mathematics, 2016 Altres ajuts: ICREA Academia We classify all of the weight-homogeneous planar polynomial differential systems of weight degree 4 having a polynomial first integral.
Llibre, Jaume, Valls, Claudia
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Discrete & Continuous Dynamical Systems - A, 2013 In this paper we find necessary and sufficient conditions in order that a planar quasi-homogeneous polynomial differential system has a polynomial or a rational first integral. We also prove that any planar quasi-homogeneous polynomial differential system can be transformed into a differential system of the form u˙ = uf(v), ˙v = g(v) with f(v) and g(v)
Giné, Jaume +2 more
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Symbolic Computations of First Integrals for Polynomial Vector Fields [PDF]
Foundations of Computational Mathematics, 2019 In this article we show how to generalize to the Darbouxian, Liouvillian and Riccati case the extactic curve introduced by J. Pereira. With this approach, we get new algorithms for computing, if it exists, a rational, Darbouxian, Liouvillian or Riccati first integral with bounded degree of a polynomial planar vector field.
Chèze, Guillaume, Combot, Thierry
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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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Darboux and rational first integrals for a family of cubic three dimensional system
Zanco Journal of Pure and Applied Sciences, 2021 In this paper, we investigate the first integrals of the following system where and , . This kind of system is a special case of three-dimensional polynomial cubic differential systems.
Sarbast H. Mikaeel , Azad I. Amen
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Unusual Nonpolynomial Van der Pol Oscillator Equations With Exact Harmonic and Isochronous Solutions
International Journal of Analysis and Applications, 2022 We do not know Van der Pol-type equations with nonlinear restoring force having explicitly an exact periodic solution. We present, for the first time, nonpolynomial Van der Pol oscillator equations that do not satisfy the classical existence theorems. We
Kolawolé Kêgnidé Damien Adjaï +3 more
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Return Probability of Quantum and Correlated Random Walks
Entropy, 2022 The analysis of the return probability is one of the most essential and fundamental topics in the study of classical random walks. In this paper, we study the return probability of quantum and correlated random walks in the one-dimensional integer ...
Chusei Kiumi, Norio Konno, Shunya Tamura
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On the number of zeros of Melnikov functions [PDF]
, 2010 We provide an effective uniform upper bond for the number of zeros of the first non-vanishing Melnikov function of a polynomial perturbations of a planar polynomial Hamiltonian vector field.
Benditkis, Sergey, Novikov, Dmitry
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Extension of germs of holomorphic foliations [PDF]
, 2014 We consider the problem of extending germs of plane holomorphic foliations to foliations of compact surfaces. We show that the germs that become regular after a single blow up and admit meromorphic first integrals can be extended, after local changes of ...
Calsamiglia, Gabriel, Sad, Paulo
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