The existence of homoclinic orbits in Hamiltonian inclusions (Q5945233)
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scientific article; zbMATH DE number 1656301
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The existence of homoclinic orbits in Hamiltonian inclusions |
scientific article; zbMATH DE number 1656301 |
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The existence of homoclinic orbits in Hamiltonian inclusions (English)
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11 April 2002
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homoclinic orbit
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Hamiltonian inclusion
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Clarke generalized gradient
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The author considers the following Hamiltonian inclusion NEWLINE\[NEWLINE\dot z(t)\in J\partial H\bigl(t,z(t)\bigr), \tag{P}NEWLINE\]NEWLINE where \(H(t,\cdot)\): \(\mathbb{R}^{2n} \to\mathbb{R}\) is locally Lipschitz continuous, \(\partial H\) is the Clarke generalized gradient of \(H\) [\textit{F. H. Clarke}, Optimization and nonsmooth analysis, New York, Wiley (1983; Zbl 0727.90045)].NEWLINENEWLINENEWLINEGeneralizing a result by \textit{F. Hofer} and \textit{K. Wysocki} [Math. Ann. 288, No. 3, 483-503 (1990; Zbl 0702.34039)], the author proves that (P) has at least one homoclinic orbit at \(0\).
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