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arXiv · 2501.05538

Equidistribution of orbits at polynomial times in rigid dynamical systems

Kosma Kasprzak
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Abstract

We study distribution of orbits sampled at polynomial times for uniquely ergodic topological dynamical systems $(X, T)$. First, we prove that if there exists an increasing sequence $(q_n)$ for which the rigidity condition \[ \max_{t 1$ a much weaker rigidity condition \[ \max_{t<q_n^{C-1}}\sup\limits_{x\in X}d\left(x, T^{tq_n}x\right)=o(1) \] implies density of all orbits $(T^{n^C}x)$ in totally uniquely ergodic systems, as long as the sequence $(\omega(q_n))$ is bounded.

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Kosma Kasprzak. 2025-01-09. Equidistribution of orbits at polynomial times in rigid dynamical systems. https://arxiv.org/abs/2501.05538

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