Sub-harmonics for two-dimensional Hamiltonian systems (Q1964790)
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scientific article; zbMATH DE number 1406548
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sub-harmonics for two-dimensional Hamiltonian systems |
scientific article; zbMATH DE number 1406548 |
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Sub-harmonics for two-dimensional Hamiltonian systems (English)
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23 February 2000
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The author proves the following result: Every asymptotically linear \(T\)-periodic Hamiltonian system in \(\mathbb{R}^2\) which has at least two periodic orbits must have infinitely many sub-harmonics, of course, in the presence of non-resonance conditions. The existence result is based on the Morse theory for the action developed by Conley and Zehnder. Note that the author's main result is strictly related to a recent result by Frank, proved by completely different methods.
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Hamiltonian system
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periodic orbits
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sub-harmonics
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Morse theory
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