Diophantine charactarization of hypoelliptic vector fields on the torus \(T^2\) (Q2759773)
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scientific article; zbMATH DE number 1683739
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Diophantine charactarization of hypoelliptic vector fields on the torus \(T^2\) |
scientific article; zbMATH DE number 1683739 |
Statements
8 August 2002
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rotation number
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Diophantine condition
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Diophantine charactarization of hypoelliptic vector fields on the torus \(T^2\) (English)
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The author considers a \(C^\infty\) smooth vector field on the torus \(\mathbb{T}^2\) interpreting it as a first-order partial differential operator (PDO) \(L_\lambda\). The the standard definition of a hypoelliptic PDO on the torus is given. It is proved in Theorem 3 that the vector field \(L_\lambda\) is hypoelliptic if and only if its rotation number satisfies some Diophantine condition.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00056].
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