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Transversal Homoclinic Orbits in an Integrable System
American Journal of Mathematics, 1978We construct a Hamiltonian system on TP' which admits a hyperbolic equilibrium point together with 2n transversal homoclinic orbits. However, the system is completely integrable, and hence X possesses no invariant subsystems topologically conjugate to the suspension of a Bernoulli shift.
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Generating Chaos with Saddle-Focus Homoclinic Orbit
International Journal of Bifurcation and ChaosThis paper develops an anticontrol approach to design a 3D continuous-time autonomous chaotic system with saddle-focus homoclinic orbit, based on two chaotification criterions for all orbits to be globally bounded with positive Lyapunov exponents.
Chaoxia Zhang +2 more
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Existence of homoclinic orbit of Shilnikov type and the application in Rössler system
Mathematics and Computers in Simulation, 2023Yuting Ding
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Computational recovery of the homoclinic orbit in porous media convection
International Journal of Non-Linear Mechanics, 1999Peter Vadasz
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An exact homoclinic orbit and its connection with the Rössler system
Physics Letters, Section A: General, Atomic and Solid State Physics, 2015Antonio Algaba
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Homoclinic orbits near heteroclinic cycles with one equilibrium and one periodic orbit
Journal of Differential Equations, 2005J D M Rademacher
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ON HOMOCLINIC AND HETEROCLINIC ORBITS OF CHEN'S SYSTEM
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2006Chen Guanrong
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