The geodesic flow of a generic metric does not admit nontrivial integrals polynomial in momenta (Q2813863)
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scientific article; zbMATH DE number 6598451
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The geodesic flow of a generic metric does not admit nontrivial integrals polynomial in momenta |
scientific article; zbMATH DE number 6598451 |
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The geodesic flow of a generic metric does not admit nontrivial integrals polynomial in momenta (English)
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27 June 2016
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geodesic flows
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polynomial in momenta integrals
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Killing tensors
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finite-dimensional integrable systems
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0.89099246
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0.8712521
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0.86944604
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0.8667413
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0.8629254
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0.8620228
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Any smooth geodesic flow is locally Liouville integrable with smooth integrals. The authors show that generically this fails if we require, in addition, that the integrals are polynomial (or, more generally, analytic) in momenta. In the article it is obtained that a generic real analytic metric does not admit, even locally, a real analytic integral.
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