Results 141 to 150 of about 5,968 (173)

Homoclinic Explosions: The First Homoclinic Explosion

1982
When r > 1 there is a two-dimensional sheet of initial values in R3 from which trajectories tend towards the origin. This two-dimensional sheet is called the stable manifold of the origin. Near the origin we know that this sheet looks like a plane (the plane associated with the two negative eigenvalues of the flow linearized near the origin) and if we ...
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Rigorous Computations of Homoclinic Tangencies

SIAM Journal on Applied Dynamical Systems, 2006
In this paper, we propose a rigorous computational method for detecting homoclinic tangencies and structurally unstable connecting orbits. It is a combination of several tools and algorithms, including the interval arithmetic, the subdivision algorithm, the Conley index theory, and the computational homology theory.
Zin Arai, Konstantin Mischaikow
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Hyperbolicity and the Creation of Homoclinic Orbits

The Annals of Mathematics, 1987
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Palis, J., Takens, F.
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ON CODING OF SERIES OF HOMOCLINIC LOOPS

International Journal of Bifurcation and Chaos, 1996
Three possible general types of origin and coding of series of complicated homoclinic saddle loops in dynamical systems with two degrees-of-freedom are pointed out. As an example of a physically important application, series of complicated vector solitons in birefringent (or bimodal) fiber governed by the system of two coupled nonlinear Schrödinger ...
Eleonsky, V. M., Korolev, V. G.
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Scaling invariance of the homoclinic tangle

Physical Review E, 2002
The structure of the homoclinic tangle of 11 / 2 degrees of freedom Hamiltonian systems in the neighborhood of the saddle point is invariant under discrete rescaling of the system's parameters. The rescaling constant is derived from the separatrix map and the Melnikov formula.
L, Kuznetsov, G M, Zaslavsky
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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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Homoclinic breather and rogue wave solutions to Maccari equation

Computers and Mathematics With Applications, 2020
Ying Jiang
exaly  

Bifurcations toN-homoclinic orbits andN-periodic orbits in vector fields

Journal of Dynamics and Differential Equations, 1993
Hiroshi Kokubu, Hiroe Oka
exaly  

Infinitely many homoclinic orbits for the second-order Hamiltonian systems

Applied Mathematics Letters, 2003
Zou Wenming
exaly  

ON HOMOCLINIC AND HETEROCLINIC ORBITS OF CHEN'S SYSTEM

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2006
Guanrong Chen, Guoting Chen
exaly