Results 201 to 210 of about 1,641 (211)

NUMERICAL COMPUTATION OF HOMOCLINIC ORBITS FOR FLOWS

International Journal of Bifurcation and Chaos, 2000
It is shown that numerical computation of homoclinic orbits for flows will generate transverse homoclinic points when one uses very accurate schemes.
Dah-Zen Wang, Whei-Ching C. Chan
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Homoclinic orbits of the Kovalevskaya top with perturbations

ZAMM, 2005
Summary: The instability issue of the permanent rotation of a heavy top is revisited and the analytical characteristic equation for the particular solution is derived. The homoclinic orbits of the Kovalevskaya top are formulated from the Kovalevskaya fundamental equation and the Kotter transformation.
Andrew Y. T. Leung, J.L. Kuang
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Infinity of minimal homoclinic orbits

Nonlinearity, 2011
In this paper, we show that there are infinitely many -semi-static homoclinic orbits to under the condition that there exists a cohomology c at the boundary of the flat such that hc(g) > 0 holds for each .
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Differential Equations with Bifocal Homoclinic Orbits

International Journal of Bifurcation and Chaos, 1997
Global bifurcation theory can be used to understand complicated bifurcation phenomena in families of differential equations. There are many theoretical results relating to systems having a homoclinic orbit biasymptotic to a stationary point at some value of the parameters, and these results depend upon the eigenvalues of the Jacobian matrix of the ...
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On homoclinic tangencies, hyperbolicity, creation of homoclinic orbits and variation of entropy

Nonlinearity, 2000
This paper generalizes a result of \textit{J.-M. Gambaudo} and \textit{J. Rocha} [ibid. 7, 1251-1259 (1994; Zbl 0806.58031), Erratum 12, 443 (1999; Zbl 0959.37028)], which gave sufficient conditions for a diffeomorphism on the 2-sphere to be \(C^1\) approximated by another exhibiting a homoclinic point, using an unproved theorem of Araújo and Mané. The
Martín Sambarino, Enrique R. Pujals
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Periodic Orbits Near Homoclinic Orbits

1982
It is known that the orbit-structure of a dynamical system near a homoclinic orbit γ is extremely complicated. However, it is only recently that this complicated structure has begun to be understood. It has been shown (under some hypotheses) that, near γ there are infinitely many long periodic orbits. The flow, near γ, admits a singular Poincare map o:
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On the existence of homoclinic orbits on Riemannian manifolds

Ergodic Theory and Dynamical Systems, 1994
AbstractWe prove the existence of a non-trivial homoclinic orbit on a Riemannian manifold (possibly non-compact), for Hamiltonian systems of the second order of the form:where the potential V is T-periodic in the time variable.
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The existence of homoclinic orbits in Hamiltonian inclusions

Nonlinear Analysis: Theory, Methods & Applications, 2001
The author considers the following Hamiltonian inclusion \[ \dot z(t)\in J\partial H\bigl(t,z(t)\bigr), \tag{P} \] where \(H(t,\cdot)\): \(\mathbb{R}^{2n} \to\mathbb{R}\) is locally Lipschitz continuous, \(\partial H\) is the Clarke generalized gradient of \(H\) [\textit{F. H.
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A Homoclinic Orbit for the Double Pendulum

1999
We consider a Hamiltonian system of two connected pendulums for the case of small mass of the second oscillator. We are interested in a homoclinic orbit for such system and present the equation for it.
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HOMOCLINIC ORBITS AND DRESSING METHOD

2007
E.V. Doktorov, Vassilios M. Rothos
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