All Questions
Tagged with ds.dynamical-systems equidistribution
7 questions
10
votes
2
answers
371
views
Refined equidistribution for the periodic trajectories of Anosov flows?
Duke, and Linnik before him under a restrictive condition, proved that the set of closed geodesics of a given length $L$ is equidistributed on the modular surface as $L \to \infty$. This is a theorem ...
- 13.8k
4
votes
0
answers
122
views
Conditions on $R\subseteq \mathbb{N}$ so that $\{\{xr\}:r\in R\}$ is dense in $[0,1]$ for all irrational $x$
A related question was posted on MSE (link), although that had some additional stipulations.
Let $S^1=\{w\in \mathbb{C}:|w|=1\}$ be the unit complex circle. Call a set $R\subseteq\mathbb{N}$ good if, ...
- 141
1
vote
1
answer
87
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Is equal natural density on intervals with matching areas but opposite signs sufficient to use fixed-width part sizes for a simple Riemann sum?
Suppose we have a sequence $\theta_n$ which is dense on $\left(0,2\pi\right)$. Furthermore, if $A=(x,y)\subset(0,\pi)$ and $B=(x+\pi,y+\pi)$ for some $x,y$, and if we define the natural density of a ...
1
vote
0
answers
84
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Coarse well-distributedness/equidistribution of Pell sequence prefixes
I am interested in the distributedness or "mixing" behavior of certain
linear recurrences modulo powers of $2$.
In particular, consider the Pell sequence (https://oeis.org/A000129),
modulo $...
- 11
1
vote
0
answers
67
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Equidistribution on subvarieties of $\mathrm{SL}_n(\mathbb{Z})$
$\DeclareMathOperator\SL{SL}$Let $\Gamma_{\infty}$ be a maximal parabolic subgroup of $\SL_n(\mathbb{Z})$. I believe there are various equidistribution theorems, which say that Iwasawa $x$ coordinates ...
- 2,907
1
vote
0
answers
87
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How fast will it converge to equilibrium？
$\alpha \in \mathbb{R} \backslash \mathbb{Q}$, given $\varepsilon>0 \quad \lambda>0$.
given $n_{1}, \cdots, n_{k} \in N^{*}$ satisfied $(1-\varepsilon) \lambda<n_{1}<\cdots<n_{k}<(1+...
- 543
1
vote
0
answers
69
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Equidistribution of linear forms over euclidean ball
Given a vector $v\in \mathbb{Z}^d\setminus\{0\}$, an irrational number $\eta$ and some big $M>0$ what type of bound can one get on $$\sum_{w\in \mathbb{Z}^d\cap B(0, M)}\exp(2\pi i \eta \cdot \...
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