Infinite-modal maps with global chaotic behavior (Q1281566)
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scientific article; zbMATH DE number 1267996
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Infinite-modal maps with global chaotic behavior |
scientific article; zbMATH DE number 1267996 |
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Infinite-modal maps with global chaotic behavior (English)
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16 June 1999
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The main goal is to study the dynamics of certain parametrized families \((f_\mu)_\mu\) of one-dimensional maps with infinite critical set. The authors show that they exhibit global chaotic behaviour in a persistent way: For a positive Lebesgue measure set of parameter values the map is transitive and almost every orbit has positive Lyapunov exponent. This class of systems is motivated by a problem in the dynamics of flows in three dimensions: the unfolding of saddle-focus homoclinic connections.
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critical set
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chaotic behaviour
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homoclinic connections
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saddle-focus homoclinic connections
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