On homoclinic orbits to center manifolds of elliptic-hyperbolic equilibria in Hamiltonian systems (Q2832527)
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scientific article; zbMATH DE number 6652195
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On homoclinic orbits to center manifolds of elliptic-hyperbolic equilibria in Hamiltonian systems |
scientific article; zbMATH DE number 6652195 |
Statements
11 November 2016
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Hamiltonian system
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saddel-center
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homoclinic orbit
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scattering map
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symplectic map
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On homoclinic orbits to center manifolds of elliptic-hyperbolic equilibria in Hamiltonian systems (English)
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Under the assumptions that a Hamiltonian system has a saddle-center equilibrium with a homoclinic orbit to the center manifold, which belongs to the intersection of the stable and unstable manifolds of the equilibrium, the authors prove that the homoclinic orbit corresponds to zeros of a certain function via a Lyapunov-Schmidt reduction procedure.
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