Diophantine and minimal but not uniquely ergodic (almost) (Q2903937)
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scientific article; zbMATH DE number 6063061
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Diophantine and minimal but not uniquely ergodic (almost) |
scientific article; zbMATH DE number 6063061 |
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Diophantine and minimal but not uniquely ergodic (almost) (English)
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2 August 2012
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minimal non-uniquely ergodic behaviour
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diophantine frequency
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singular time
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The aim of the present paper is to show that minimal non-uniquely ergodic behaviour can be generated by slowing down a simple harmonic ascillator with diophantine frequency, in contrast with the known examples where the frequency is well approximable by the rationals. The result is effected by a singular time change that brings one phase point to rest. The time-one map of the flow have uncountably many invariant measures yet every orbit is dense, with the minor exception of the rest point.
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