List questions from ergodic-theory

Published on 22 Mar 2026 - 14:53

136

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Inequality involving power to fractional part of integer multiples of logarithm of integer to coprime base.

Published on 23 Mar 2026 - 2:58

533

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Show that the digit $d$($0<d<10$) occurs as a first digit in power of 2 with frequency $log_{10} \frac{d+1}{d}$.

Published on 17 Feb 2018 - 18:15

69

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Give a countable set of periodic points of $T$ where $\Bbb T=[0,1)/\{0=1\}$

Published on 17 Mar 2026 - 22:07

37

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Does this stochastic convergence hold?

Published on 22 Mar 2026 - 6:38

132

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Simple Billiard Table with Positive Lyapunov exponent

Published on 24 Mar 2026 - 20:20

43

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What is the frequency of $w$ appearing in the binary expansion of almost every $x \in (0,1)\setminus \{ \frac p{2^n}: 0<p<2^n; n\geq 1\}$

Published on 22 Feb 2018 - 10:22

434

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Can a hyperbolic fixed point be inside a homoclinic loop on a plane?

Published on 23 Mar 2026 - 8:18

24

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Prove that $w(x)$ the derived set of $O_T^+(x)$ is $X$.

Published on 23 Feb 2018 - 18:53

117

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Prove that the closure of every $T$-orbit is a $T$-invariant subset of X

Published on 23 Feb 2018 - 19:20

98

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prove that $O_T(0)=\{na\pmod 1: n \in \Bbb Z\}$ is dense in $[0,1)$.

Published on 24 Feb 2018 - 18:41

728

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Generic point - invariant measure

Published on 21 Mar 2026 - 22:03

128

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Ergodic system counterexample

Published on 20 Mar 2026 - 3:50

234

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Prove that the set $[0,1]\setminus E$ has Lebesgue measure zero.

Published on 25 Feb 2018 - 18:36

69

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Prove that $T$ has a minimal set and list countably many minimal sets of $T$.

Published on 26 Feb 2018 - 11:55

List Question

Is the sequence equidistributed on the sphere?

Inequality involving power to fractional part of integer multiples of logarithm of integer to coprime base.

Show that the digit $d$($0<d<10$) occurs as a first digit in power of 2 with frequency $log_{10} \frac{d+1}{d}$.

Give a countable set of periodic points of $T$ where $\Bbb T=[0,1)/\{0=1\}$

Does this stochastic convergence hold?

Simple Billiard Table with Positive Lyapunov exponent

What is the frequency of $w$ appearing in the binary expansion of almost every $x \in (0,1)\setminus \{ \frac p{2^n}: 0<p<2^n; n\geq 1\}$

Can a hyperbolic fixed point be inside a homoclinic loop on a plane?

Prove that $w(x)$ the derived set of $O_T^+(x)$ is $X$.

Prove that the closure of every $T$-orbit is a $T$-invariant subset of X

prove that $O_T(0)=\{na\pmod 1: n \in \Bbb Z\}$ is dense in $[0,1)$.

Generic point - invariant measure

Ergodic system counterexample

Prove that the set $[0,1]\setminus E$ has Lebesgue measure zero.

Prove that $T$ has a minimal set and list countably many minimal sets of $T$.

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