Transversal homoclinic intersection

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A Geometric Criterion for the Existence of Chaos Based on Periodic Orbits in Continuous-Time Autonomous Systems

Journal of dynamical and control systems, 2019
A new geometric criterion is derived for the existence of chaos in continuous-time autonomous systems in three-dimensional Euclidean spaces, where a type of Smale horseshoe in a subshift of finite type exists, but the intersection of stable and unstable ...
Xu Zhang, Guanrong Chen
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Stability of Multi-Degree of Freedom Stochastic Nonlinear Systems

Nonlinear Dynamics and Controls, 1996
Melnikov’s method for finding necessary conditions for homoclinic chaos is extended to a class of stochastically forced multi-degree of freedom nonlinear systems.
T. Whalen
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Homoclinic bifurcation in a quasiperiodically excited impact inverted pendulum

Nonlinear dynamics, 2015
Junming Gao, Zheng-Dong Du
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Symbolic Dynamics Near a Transversal Homoclinic Orbit of a System of Ordinary Differential Equations

, 2000
K. Palmer
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Transversal intersection of separatrices, the structure of the set of quasi-stochastic motions and the non-existence of an analytic integral in multidimensional systems

, 1996
S A Dovbysh
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Suppressing homoclinic chaos for a class of vibro-impact oscillators by non-harmonic periodic excitations

Nonlinear dynamics
Shuangbao Li, Rui Xu, Liying Kou
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Homoclinic Solutions to Infinity and Oscillatory Motions in the Restricted Planar Circular Three Body Problem

, 2013
M. Guardia, Pau Martín, T. Seara
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Intersection of separatrices and the non-integrability of multidimensional systems

, 2000
S A Dovbysh
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