Results 191 to 200 of about 1,641 (211)

Conventional multipliers for homoclinic orbits

Nonlinearity, 1996
Summary: We introduce and describe conventional multipliers, a new characteristic of homoclinic orbits of saddle-node type periodic trajectories. We prove existence and smooth dependence of conventional multipliers on the initial point. We show that multipliers of periodic trajectories arising from the homoclinic ones as a result of the saddle-node ...
Afraimovich, Valentine, Liu, Weishi, Young, Todd R.   +2 more
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Homoclinic orbits and chaos in discretized perturbed NLS systems: Part I. Homoclinic orbits [PDF]

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 ...
Yanguang Charles Li, David W. McLaughlin
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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
Carles Simó, V. F. Lazutkin
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Homoclinic orbits of a Hamiltonian system

Zeitschrift für angewandte Mathematik und Physik, 1999
The authors are interested in the existence of homoclinic orbits of the Hamiltonian system \(\dot x= JH_z(t,z)\) where \(z=(p,q)\in \mathbb{R}^N\times \mathbb{R}^N\), \(J\) is the standard symplectic matrix in \(\mathbb{R}^{2N}\), \(J= \left( \begin{smallmatrix} 0 &-\text{Id}\\ \text{Id} &0 \end{smallmatrix} \right)\), and \(H\in C(\mathbb{R}\times ...
Yanheng Ding, Michel Willem
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Homoclinic orbits to parabolic points

Nonlinear Differential Equations and Applications, 1997
This paper concerns non-Hamiltonian perturbations of Hamiltonian systems. Using Poincaré-Melnikov method, orbits which are homoclinic to degenerate periodic orbits of parabolic type are studied, specially the existence of transversal homoclinic points. The method used in this paper is related to a work of \textit{E.
Ana Nunes, J. Casasayas, Ernest Fontich
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Homoclinic orbits of invertible maps

Nonlinearity, 2002
The authors describe two methods of approximation of homoclinic trajectories of a saddle fixed point for a discrete dynamical system. Both methods are based on reduction of the problem to the search for homoclinic trajectories with special symmetries for some systems of higher dimension. As examples, a cubic map and the Hénon map are considered.
J M Bergamin, Tassos Bountis, Michael N. Vrahatis   +2 more
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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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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 ...
openaire   +3 more sources