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Results tagged with ds.dynamical-systems
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user 169474
Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.
2
votes
Accepted
Is equal natural density on intervals with matching areas but opposite signs sufficient to u...
Let us take the $\theta_n$ in the interval $[0,2\pi)$.
For every $N \ge 1$, set
$$\mu_N = \frac1N\sum_{n=1}^N\delta_{\theta_n} \text{ and } \nu_N := \mathbb{1}_{(0,\pi)\cup(\pi,2\pi)}\mu_N.$$
The exis …
- 3,808
7
votes
Accepted
Central limit theorem for irrational rotations
I am surprised by the question. The sums are bounded if $\alpha \ne 1$, since for every $n \ge 1$,
$$\Big|\sum_{k=1}^n \Re R_\alpha^k z \Big|
= \Big|\Re \Big(\sum_{k=1}^n R_\alpha^k z \Big) \Big| = \B …
- 3,808