Results 151 to 160 of about 6,930 (179)
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Center and isochronous center problems for quasi analytic systems
Acta Mathematica Sinica, English Series, 2008Consider the planar quasi-analytic systems \[ \begin{aligned} {dx\over dt} &=\delta x- y+ \sum^\infty_{k=2} (x^2+ y^2)^{(k-1)(\lambda- 1)/2}X_k(x,y),\\ {dy\over dt} &= x+\delta y+ \sum^\infty_{k=2} (x^2+ y^2)^{(k-1)(\lambda- 1)/2} Y_k(x, y),\end{aligned} \] where \[ \begin{aligned} X_k(x, y) &= \sum_{\alpha+\beta= k} A_{\alpha\beta} x^\alpha y^\beta,\\
Liu, Yi Rong, Li, Ji Bin
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Isochronous centers and flat Finsler metrics (I)
Canadian Journal of MathematicsAbstractThe local structure of rotationally symmetric Finsler surfaces with vanishing flag curvature is completely determined in this paper. A geometric method for constructing such surfaces is introduced. The construction begins with a planar vector field X that depends on two functions of one variable.
Xinhe Mu, Hui Miao, Libing Huang
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Isochronous centers of cubic reversible systems
2008In this paper we study isochronous centers of reversible two-dimensional autonomous system with linear part of center type and nonlinear part given by polynomials of third degree. Firstly we find necessary conditions for such isochronous centers in polar coordinates and finally we give a proof of the isochronicity of these systems using different ...
Javier Chavarriga, Isaac García
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Bifurcation of Critical Periods from a Quartic Isochronous Center
International Journal of Bifurcation and Chaos, 2014This paper is focused on the bifurcation of critical periods from a quartic rigidly isochronous center under any small quartic homogeneous perturbations. By studying the number of zeros of the first several terms in the expansion of the period function in ε, it shows that under any small quartic homogeneous perturbations, up to orders 1 and 2 in ε ...
Peng, Linping, Feng, Zhaosheng
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Number of Critical Periods for Perturbed Rigidly Isochronous Centers
International Journal of Bifurcation and Chaos, 2016This paper deals with the bifurcation of critical periods from a rigidly quartic isochronous center. It shows that under any small homogeneous perturbation of degree four, up to any order in [Formula: see text], there are at most two critical periods bifurcating from the periodic orbits of the unperturbed system, and the upper bound is sharp.
Lu, Lianghaolong +2 more
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Centers and Isochronous Centers of Newton Systems with Force Function Quadratic in Velocities
Differential Equations, 2019Necessary and sufficient conditions are obtained for a center as well as an isochronous center of holomorphic Newton equations with force function quadratic in velocities.
Amel'kin, V. V., Rudenok, A. E.
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Isochronicity of centers in some planar differential systems
SCIENTIA SINICA Mathematica, 2016For planar differential systems the isochronicity of centers, as a continuation of the center problem, relates to the synchronism of periodic oscillations. In this paper we introduce recent results and basic methods on isochronicity of nondegenerate centers for planar differential systems including homogeneous systems, reversible systems, and ...
CHEN XingWu, ZHANG WeiNian, WANG ZhaoXia
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Commutators and linearizations of isochronous centers
2000The authors study isochronous centers of some classes of plane differential systems. They consider systems with constant angular speed, both with homogeneous and nonhomogeneous nonlinearities, and show how to construct linearizations and first integrals to such systems, if a commutator is known.
Sabatini, Marco, L. Mazzi
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Cancer risk among World Trade Center rescue and recovery workers: A review
Ca-A Cancer Journal for Clinicians, 2022Paolo Boffetta +2 more
exaly
The isochronous center for Kukles homogeneous systems of degree eight
Applied Mathematics Letters, 2023Yusen Wu
exaly