Results 221 to 230 of about 8,908 (255)

The Numerical Computation of Homoclinic Orbits for Maps

SIAM Journal on Numerical Analysis, 1997
Summary: Transversal homoclinic orbits of maps are known to generate shift dynamics on a set with Cantor-like structure. In this paper a numerical method is developed for computation of the corresponding homoclinic orbits. They are approximated by finite-orbit segments subject to asymptotic boundary conditions.
Beyn, Wolf-Jürgen, Kleinkauf, J. M.
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Orbits homoclinic to resonances: The Hamiltonian case [PDF]

Physica D: Nonlinear Phenomena, 1993
The authors consider a Hamiltonian two-degree-of-freedom system which is integrable and has a two-dimensional normally hyperbolic invariant manifold filled with periodic orbits. For perturbations of the system they establish an energy-phase criterion which gives a complete picture of the dynamics associated with orbits homoclinic to the resonance.
György Haller, Stephen Wiggins
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Existence of optimal homoclinic orbits [PDF]

2008 American Control Conference, 2008
The problem of optimal periodic control is considered from a geometric point of view. The objective is to determine the conditions under which a given optimal control problem admits a homoclinic orbit as an extremal solution. The analysis is performed on the Hamiltonian dynamical system obtained from the application of Pontryagin Maximum Principle ...
Nicolas Hudon, Kai Höffner, Martin Guay
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N-Homoclinic bifurcations for homoclinic orbits changing their twisting

Journal of Dynamics and Differential Equations, 1996
The author considers two-parameter families of vector fields possessing a homoclinic orbit along a path in the parameter plane. These homoclinic orbits are homoclinic to a hyperbolic singularity that has a one-dimensional unstable manifold. The weakest stable and unstable eigenvalues of the linearized vector field at the singularity are supposed to be ...
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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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