Uniform hyperbolicity along periodic orbits (Q2845460)
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scientific article; zbMATH DE number 6203439
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Uniform hyperbolicity along periodic orbits |
scientific article; zbMATH DE number 6203439 |
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Uniform hyperbolicity along periodic orbits (English)
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30 August 2013
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hyperbolicity along periodic orbits
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homoclinic class
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dominated splitting
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uniform hyperbolicity
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0.90805495
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0.90046775
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0.89487475
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0.8872067
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The paper under review is a very interesting work where the author introduces the notion of uniform hyperbolicity along periodic orbits (UHPO) for homoclinic classes.NEWLINENEWLINE The paper provides equivalent conditions under which the UHPO property on a \(C^1\)-generic homoclinic class implies hyperbolicity. Moreover, it is shown that for a \(C^1\)-generic locally maximal homoclinic class, the UHPO property is equivalent to the nonexistence of zero Lyapunov exponents. Using the notion of UHPO, a new proof is given for some recent \(C^1\)-dichotomy theorems.
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