Self-similar constructions in smooth dynamics: Rigidity, smoothness and dimension (Q1208341)
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scientific article; zbMATH DE number 166306
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Self-similar constructions in smooth dynamics: Rigidity, smoothness and dimension |
scientific article; zbMATH DE number 166306 |
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Self-similar constructions in smooth dynamics: Rigidity, smoothness and dimension (English)
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16 May 1993
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The relationship between rigidity, smoothness and dimension in smooth dynamics is investigated with the aid of some simple examples of smooth maps at the accumulation of cascades of period doubling bifurcation. It is shown that the minimal smoothness required to hope for universality at the accumulation of period doubling bifurcations increases with the dimension. Some applications concerning \(C^ 2\) diffeomorphisms of the two-disk with zero entropy having infinitely many periodic orbits are presented.
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dynamical systems
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smooth dynamics
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self-similarity
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period-doubling bifurcation
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universality in physics
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0.8727149
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0.8715818
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0.8665667
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