Homotopy and dynamics for homeomorphisms of solenoids and Knaster continua (Q2717757)
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scientific article; zbMATH DE number 1605345
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Homotopy and dynamics for homeomorphisms of solenoids and Knaster continua |
scientific article; zbMATH DE number 1605345 |
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Homotopy and dynamics for homeomorphisms of solenoids and Knaster continua (English)
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17 June 2001
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homotopy class
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topological entropy
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solenoid
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0.91152143
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0.9014424
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0.8984629
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0.8968937
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0.8915175
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The homotopy class of self-homeomorphisms of 1-dimensional solenoids and Knaster continua are described, and it is shown that the topological entropy is constant on each class. Moreover, the homeomorphisms in a class of positive entropy are shown to be semi-conjugate to an algebraic homeomorphism. The topological entropy is computed using fiber entropies and an extension of some of \textit{R. Bowen}'s entropy calculation [Trans. Am. Math. Soc. 153, 401-414 (1971; Zbl 0212.29201)], avoiding the harmonic analysis and adelic covering of the approach by \textit{D. A. Lind} and the reviewer [Ergodic Theory Dyn. Syst. 8, No. 3, 411-419 (1988; Zbl 0634.22005)].
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