A note on the isomorphism of Cartesian products of ergodic flows

Kułaga, Joanna

doi:10.1007/s10883-012-9142-7

Cited by 2 publications

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References 19 publications

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“…We generalize one of the facts from [5] on the isomorphism of flows and give a negative response to the mentioned question in the situation where systems are not required to both be ergodic. We first start with these examles.…”

Section: Introductionmentioning

confidence: 99%

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Thouvenot’s Isomorphism Problem for Tensor Powers of Ergodic Flows

Ryzhikov

2018

Math Notes

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Key words. Measure-preserving flows, tensor powers of dynamical systems, measure-theoretical isomorphism. AbstractThe following question due to Thouvenot is well-known in ergodic theory. Let S and T be automorphisms of a probability space and S ⊗ S be isomorphic to T ⊗ T . Will S and T be isomorphic? Our note contains a simple answer to this question and a generalization of Kulaga's result on the corresponding isomorphism within a class of flows. We show that the isomorphism of weakly mixing flows S t ⊗ S t and T t ⊗ T t implies the isomorphism of the flows S t and T t , if one of them has an integral weak limit.

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Section: Introductionmentioning

confidence: 99%

“…Main result. In [5], in particular, it is proved that the isomorphism of flows S t ⊗ S t T t ⊗ T t implies the isomorphism of the flows S t and T t , if the flow T t has a weak limit in the form R T a dν(a), where ν is a continuous mesure on R with analytical Fourier transform. We shall show that this last condition is not necessary.…”

Section: Introductionmentioning

confidence: 99%

Thouvenot’s Isomorphism Problem for Tensor Powers of Ergodic Flows

Ryzhikov

2018

Math Notes

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Задача Тувено Об Изоморфизме Тензорных Степеней Эргодических Потоков

Ryzhikov¹

2018

Matematicheskie Zametki

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Пусть $S$ и $T$ - автоморфизмы вероятностного пространства, а их степени $S \otimes S$ и $T \otimes T$ изоморфны. Будут ли изоморфны автоморфизмы $S$ и $T$? Этот вопрос Тувено хорошо известен в эргодической теории. Заметка содержит ответ на него и обобщение одного из результатов Кулаги об изоморфизме в случае потоков. Показано, что изоморфизм слабо перемешивающих потоков $S_t \otimes S_t$ и $T_t \otimes T_t$ влечет за собой изоморфизм потоков $S_t$ и $T_t$, если один из этих потоков обладает интегральным слабым пределом. Библиография: 12 названий.

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A note on the isomorphism of Cartesian products of ergodic flows

Abstract: We show an isomorphism stability property for Cartesian products of either flows with joining primeness property or flows which are α-weakly mixing.

Cited by 2 publications

References 19 publications

Thouvenot’s Isomorphism Problem for Tensor Powers of Ergodic Flows

Thouvenot’s Isomorphism Problem for Tensor Powers of Ergodic Flows

Задача Тувено Об Изоморфизме Тензорных Степеней Эргодических Потоков

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