The geodesic flow: The Frida Kahlo of mathematics (Q2771070)
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scientific article; zbMATH DE number 1705180
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The geodesic flow: The Frida Kahlo of mathematics |
scientific article; zbMATH DE number 1705180 |
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17 February 2003
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geodesic flow
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hyperbolic geometry
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natural foliations
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hyperbolic disk
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Anosov decomposition
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0.8458994
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0.8162057
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The geodesic flow: The Frida Kahlo of mathematics (English)
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This text is a brief introduction to the notion of geodesic flow and its properties, centered in the case of 2-dimensional hyperbolic geometry. The mathematical prerequisites are minimal. Understanding of the main features of hyperbolic geometry is made easier by comparison with Euclidean geometry. NEWLINENEWLINENEWLINEThe author starts with an introduction to 2-dimensional hyperbolic geometry. The notions of unitary tangent space, geodesic flow and natural foliations of the hyperbolic disk are presented. The structural stability of the geodesic flow is discussed, using the Anosov decomposition and the classical Shadowing Lemma. The text concludes with a brief introduction to the Hopf Ergodic Theorem for hyperbolic surfaces.NEWLINENEWLINEFor the entire collection see [Zbl 0948.00039].
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