Results 121 to 130 of about 467 (169)

Controlling homoclinic orbits

Theoretical and Computational Fluid Dynamics, 1989
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Bloch, A. M., Marsden, J. E.
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The Dynamical Core of a Homoclinic Orbit

Regular and Chaotic Dynamics, 2022
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Hyperbolicity and the Creation of Homoclinic Orbits

The Annals of Mathematics, 1987
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Palis, J., Takens, F.
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Homoclinic Orbits in the Complex Domain

International Journal of Bifurcation and Chaos, 1997
We consider the standard map, as a paradigm of area preserving map, when the variables are taken as complex. We study how to detect the complex homoclinic points, which cannot dissappear under a homoclinic tangency. This seems a promising tool to understand the stochastic zones of area preserving maps. The paper is mainly phenomenological and includes
Lazutkin, V. F., Simó, C.
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Existence of optimal homoclinic orbits

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 Hoffner, Martin Guay
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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.
Whei-Ching C. Chan, Dah-Zen Wang
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Homoclinic orbits and chaos in discretized perturbed NLS systems: Part I. Homoclinic orbits

Journal of Nonlinear Science, 1997
The authors study the \(N\)-particle dynamical system \[ iq_{n} = (1/h^{2}) [ q_{n+1} - 2q_{n} + q_{n-1} ] + |q_{n}|^{2}(q_{n+1} + q_{n-1}) \] \[ -2\omega^{2}q_{n} + i\epsilon [ -\alpha q_{n} + (\beta / h^{2}) (q_{n+1} - 2q_{n} + q_{n-1}) + \Gamma ], \quad q_{n+N} = q_{n}, q_{N-n} = q_{n}, \] where \(i = \sqrt{-1}\), which is a finite difference ...
Li, Y., McLaughlin, D. W.
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ON HOMOCLINIC AND HETEROCLINIC ORBITS OF CHEN'S SYSTEM

International Journal of Bifurcation and Chaos, 2006
We study the problem of existence of homoclinic and heteroclinic orbits of Chen's system. For the case of 2c > a > c > 0 and b ≥ 2a, we prove that the system has no homoclinic orbit but has two and only two heteroclinic orbits.
Tiecheng Li, Guoting Chen, Guanrong Chen
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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
Pujals, Enrique R., Sambarino, Martín
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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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