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Dynamics of Klein-Gordon on a compact surface near an homoclinic orbit

, 2014
Benoît Grébert, Tiphaine Jézéquel, Laurent Thomann   +2 more
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Hyperbolicity and the Creation of Homoclinic Orbits

The Annals of Mathematics, 1987
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Floris Takens, Jacob Palis
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Controlling homoclinic orbits

Theoretical and Computational Fluid Dynamics, 1989
In this paper we analyze various control-theoretic aspects of a nonlinear control system possessing homoclinic or heteroclinic orbits. In particular, we show that for a certain class of nonlinear control system possessing homoclinic orbits, a control can be found such that the system exhibits arbitrarily long periods in a neighborhood of the homoclinic.
Jerrold E. Marsden, Jerrold E. Marsden, Anthony M. Bloch, Anthony M. Bloch   +3 more
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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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