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Periodic solutions of a galactic potential [PDF]
Chaos, Solitons & Fractals, 2014 We study analytically the periodic solutions of a Hamiltonian in R^6 given by the kinetic energy plus a galactic potential, using averaging theory of first order. The model perturbs a harmonic oscillator, and has been extensively used in order to describe local motion in galaxies near an equilibrium point.
Llibre, Jaume +2 more
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ON PERIODIC SOLUTIONS OF 2-PERIODIC LYNESS' EQUATIONS [PDF]
International Journal of Bifurcation and Chaos, 2013 We study the existence of periodic solutions of the nonautonomous periodic Lyness' recurrenceun+2 = (an + un+1)/un, where {an}n is a cycle with positive values a, b and with positive initial conditions. It is known that for a = b = 1 all the sequences generated by this recurrence are 5-periodic.
Bastien, Guy +2 more
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Periods of solutions of periodic differential equations
Differential and Integral Equations, 2016 Smooth non-autonomous T-periodic differential equations x'(t)=f(t,x(t)) defined in \R\K^n, where \K is \R or \C and n 2 can have periodic solutions with any arbitrary period~S. We show that this is not the case when n=1. We prove that in the real C^1-setting the period of a non-constant periodic solution of the scalar differential equation is a divisor
Cima, Anna +2 more
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Periods of periodic solutions and the Lipschitz constant [PDF]
Proceedings of the American Mathematical Society, 1969 let x = -Lx2, X2 = Lxi, x =0 for 2 < i < n, then (2) is satisfied letting F(x) = (-Lx2, Lxl, 0, * * *, 0), and all nonconstant solutions are periodic with period 2wr/L. To prove the theorem, we define the functions f(t) = F(x(t)) and N(t) = f(t)I| and y(t) =f(t)/N(t), for tER. The function y(t) is a unit vector tangent to the periodic trajectory.
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Periodic solutions of periodic difference equations
Advanced Studies in Pure Mathematics, 2019 In this paper, we discuss the existence of periodic solutions of the periodic difference equation $$ x(n + 1) = f(n, x(n)),\ \ n \in \mathbf{Z} $$ and the periodic difference equation with finite delay $$ x(n + 1) = f(n, x_n),\ \ n \in \mathbf{Z}, $$ where $x$ and $f$ are $d$-vectors, and $\mathbf{Z}$ denotes the set of integers.
Furumochi, Tetsuo, Muraoka, Masato
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Degree, quaternions and periodic solutions
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2021 The paper computes the Brouwer degree of some classes of homogeneous polynomials defined on quaternions and applies the results, together with a continuation theorem of coincidence degree theory, to the existence and multiplicity of periodic solutions of a class of systems of quaternionic valued ordinary differential equations.
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Bifurcation of periodic solutions
Journal of Mathematical Analysis and Applications, 1979 Mechanical and electrical phenomena which can be described mathematically by the bifurcation or appearance of periodic solutions of a nonlinear ordinary different equation when some parameter is varied have been well-known for many years. See Minorsky [7].
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On the coexistence of periodic solutions
Journal of Differential Equations, 1970 (p(t; A)) wYyldt2 = > 5 = Pk 4Y, where X is a real parameter, and, for every /\, p(t; h) are real continuous periodic functions with period n defined for all t E (---co, 03). The problem of the coexistence of periodic solutions consists of studying such values of parameter h for which two linearly independent and periodic or hay-periodic1 solutions ...
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Discontinuous bifurcations of periodic solutions
Mathematical and Computer Modelling, 2002 This paper discusses different aspects of bifurcations of periodic solutions in discontinuous systems. It is explained how jumps in the fundamental solution matrix leadto jumps of the Floquet multipliers of periodic solutions. A Floquet multiplier of a discontinuous system can jump through the unit circle causing a discontinuousbifurcation.
D.H. van Campen, Remco I. Leine
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PERIODIC SOLUTIONS AND SLOW MANIFOLDS [PDF]
International Journal of Bifurcation and Chaos, 2007 After reviewing a number of results from geometric singular perturbation theory, we give an example of a theorem for periodic solutions in a slow manifold. This is illustrated by examples involving the van der Pol-equation and a modified logistic equation.
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