List questions from ergodic-theory

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147

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

Published on 07 May 2026 - 11:27

538

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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 29 Apr 2026 - 12:54

74

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

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42

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Does this stochastic convergence hold?

Published on 29 Apr 2026 - 12:54

141

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Simple Billiard Table with Positive Lyapunov exponent

Published on 30 Apr 2026 - 15:49

48

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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 29 Apr 2026 - 12:54

446

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

Published on 03 May 2026 - 17:35

30

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

Published on 29 Apr 2026 - 12:54

121

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

Published on 29 Apr 2026 - 12:54

102

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

Published on 29 Apr 2026 - 12:53

737

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Generic point - invariant measure

Published on 29 Apr 2026 - 12:53

135

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Ergodic system counterexample

Published on 04 May 2026 - 2:17

238

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

Published on 29 Apr 2026 - 12:53

73

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

Published on 29 Apr 2026 - 12:53

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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