Unbounded growth of energy in periodic perturbations of geodesic flows of the torus (Q2724627)
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scientific article; zbMATH DE number 1618072
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Unbounded growth of energy in periodic perturbations of geodesic flows of the torus |
scientific article; zbMATH DE number 1618072 |
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2000
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Arnold diffusion
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Unbounded growth of energy in periodic perturbations of geodesic flows of the torus (English)
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This note contains a sketch of a geometrical proof for the following theorem. For every \(r\geq15\) there is a \(C^r\)-residual set in the set of metrics \(g\) on the torus \({\mathbb T}^2\) and of time-periodic potentials \(U:{\mathbb T}^3\to {\mathbb R}\), such that the Hamiltonian \(H(q,p,t)={1\over2}g_q(p,p)+U(q,t)\) has an orbit of unbounded energy.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00039].
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