Results 141 to 150 of about 481 (186)

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 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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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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The existence of homoclinic orbits to saddle-focus

Applied Mathematics and Computation, 2005
The authors deal with the existence of homoclinic orbits to saddle-focus. To this end they present an improved version of the existence criterion for such homoclinic orbits to saddle-focus. Based on this criterion, the authors correct the result of \textit{T. Zhou}, \textit{G. Chen} and \textit{Q.
Desheng Shang, Maoan Han
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PERIODIC AND HOMOCLINIC ORBITS IN A TWO-PARAMETER UNFOLDING OF A HAMILTONIAN SYSTEM WITH A HOMOCLINIC ORBIT TO A SADDLE-CENTER

International Journal of Bifurcation and Chaos, 1995
For a two-degrees-of-freedom Hamiltonian system with a homoclinic orbit (loop) to a saddle-center we prove that the Poincaré map on a section to the loop within the Hamiltonian level containing a saddle-center is a twist map with discontinuity at the point of intersection with the loop.
Koltsova, O. Yu., Lerman, L. M.
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