Homoclinic orbits - Open Access .click

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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Controlling homoclinic orbits

Theoretical and Computational Fluid Dynamics, 1989
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Bloch, A. M., Marsden, J. E.
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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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MULTIPLE HOMOCLINIC BIFURCATIONS FROM ORBIT-FLIP I: SUCCESSIVE HOMOCLINIC DOUBLINGS

International Journal of Bifurcation and Chaos, 1996
The purpose of this and forthcoming papers is to obtain a better understanding of complicated bifurcations for multiple homoclinic orbits. We shall take one particular type of codimension two homoclinic orbits called orbit-flip and study bifurcations to multiple homoclinic orbits appearing in a tubular neighborhood of the original orbit-flip. The main
Kokubu, Hiroshi, Komuro, Motomasa, Oka, Hiroe +2 more
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homoclinic orbit
mathematics
hamiltonian system

hamiltonian systems
analysis
symbolic dynamics

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perturbations of ordinary differential equations
bifurcation