Question

Simplest proof that exactness implies mixing

score 80 · Answer 1 · 2026-03-25 20:33:58

80

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Simplest proof that exactness implies mixing

Published on 25 Mar 2026 - 20:33

score 44 · Answer 2 · 2024-03-22 17:17:38

44

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Show that $\frac{1}{n}\sum_{j=1}^n T^jx$ converges. $T: \ell^2\to \ell^2$ with $T(x_n) = (a_nx_n)_{n\geq 1}$, $\sup \lvert a_n \rvert \leq 1$

Published on 22 Mar 2024 - 17:17

score 15 · Answer 3 · 2024-03-23 10:28:57

15

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Projecting onto the Kronecker factor

Published on 23 Mar 2024 - 10:28

score 58 · Answer 4 · 2026-03-25 05:36:07

58

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Why are rotation numbers not homomorphic?

Published on 25 Mar 2026 - 5:36

score 18 · Answer 5 · 2026-03-19 06:55:16

18

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Kingsman subaddtive Ergodic theorem for continuous $f$

Published on 19 Mar 2026 - 6:55

score 35 · Answer 6 · 2024-03-29 03:02:04

35

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Convergence of measures in symbolic dynamics

Published on 29 Mar 2024 - 3:02

score 65 · Answer 7 · 2024-03-29 22:57:00

65

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Applications, Generalisations and developments of Green-Tao Theorem after 2018

Published on 29 Mar 2024 - 22:57

score 22 · Answer 8 · 2024-03-31 16:17:24

22

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Non-uniform averages for ergodic theorem

Published on 31 Mar 2024 - 16:17

score 32 · Answer 9 · 2024-03-31 18:56:06

32

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Relationship between SRB measures and invariant measures that are absolutely continuous with respect to Lebesgue measure

Published on 31 Mar 2024 - 18:56

score 39 · Answer 10 · 2024-03-31 21:31:15

39

Views

Does every $\sigma$-homomorphism of a probability algebra come from a measure preserving transformation on the probability space?

Published on 31 Mar 2024 - 21:31

score 475 · Answer 11 · 2015-01-10 16:40:36

475

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if $f$ is weakly mixing then $f^n$ is ergodic?

Published on 10 Jan 2015 - 16:40

score 764 · Answer 12 · 2015-01-13 03:17:56

764

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why a minimal dynamical system is a ergodic measure-preserving system?

Published on 13 Jan 2015 - 3:17

score 132 · Answer 13 · 2015-01-15 22:42:12

132

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Prove existence of Borel set related to the function $f(x)=2x \mod 1$

Published on 15 Jan 2015 - 22:42

score 147 · Answer 14 · 2015-01-18 06:48:49

147

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Can one generate a sequence of natural numbers whose density has a given distribution?

Published on 18 Jan 2015 - 6:48

score 397 · Answer 15 · 2026-03-26 08:14:30

397

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Strongly mixing uniquely ergodic dynamical system

Published on 26 Mar 2026 - 8:14

List Question

Simplest proof that exactness implies mixing

Show that $\frac{1}{n}\sum_{j=1}^n T^jx$ converges. $T: \ell^2\to \ell^2$ with $T(x_n) = (a_nx_n)_{n\geq 1}$, $\sup \lvert a_n \rvert \leq 1$

Projecting onto the Kronecker factor

Why are rotation numbers not homomorphic?

Kingsman subaddtive Ergodic theorem for continuous $f$

Convergence of measures in symbolic dynamics

Applications, Generalisations and developments of Green-Tao Theorem after 2018

Non-uniform averages for ergodic theorem

Relationship between SRB measures and invariant measures that are absolutely continuous with respect to Lebesgue measure

Does every $\sigma$-homomorphism of a probability algebra come from a measure preserving transformation on the probability space?

if $f$ is weakly mixing then $f^n$ is ergodic?

why a minimal dynamical system is a ergodic measure-preserving system?

Prove existence of Borel set related to the function $f(x)=2x \mod 1$

Can one generate a sequence of natural numbers whose density has a given distribution?

Strongly mixing uniquely ergodic dynamical system

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