Homoclinic and heteroclinic solutions for a class of two-dimensional Hamiltonian systems (Q1909921)
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scientific article; zbMATH DE number 859676
| Language | Label | Description | Also known as |
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| English | Homoclinic and heteroclinic solutions for a class of two-dimensional Hamiltonian systems |
scientific article; zbMATH DE number 859676 |
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Homoclinic and heteroclinic solutions for a class of two-dimensional Hamiltonian systems (English)
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24 March 1996
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The authors consider a two-dimensional Hamiltonian system with Hamiltonian \(H(x,y)\). It is assumed that \(H\) has special canyon-like structure (roughly speaking, this means that the graph of \(H\) is diffeomorphic to the lower part of a horizontal cylinder). For example, \(H(x,y) = y^2/2 + V(x)\) with \(V \in C^2\) has this structure if \(V'\) has at least two zeros. Special matrices are constructed. These matrices determine the existence of homoclinic and heteroclinic trajectories.
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homoclinic trajectories
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two-dimensional Hamiltonian system
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homoclinic
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heteroclinic trajectories
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