T. Persson

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20242026

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math.DS2026

Visiting time statistics

Maxim Kirsebom, Philipp Kunde, Tomas Persson

Many mixing dynamical systems $(X, T, I^¼)$ are known to satisfy the hitting time statistics result \[ \lim_{r \to 0} Î¼\{\, x : Ï_{B(y,r)} (x) > t/Î¼(B(y,r))\,\} = e^{-t}, \] for $Î…

math.DS2025

Almost sure orbits closeness

Maxim Kirsebom, Philipp Kunde, Tomas Persson +1

We consider the minimal distance between orbits of measure preserving dynamical systems. In the spirit of dynamical shrinking target problems we identify distance rates for which a…

math.DS2025

Strong Borel--Cantelli Lemmas for Recurrence

Tomas Persson, Alejandro Rodriguez Sponheimer

Let $(X, T, I^¼, d)$ be a metric measure-preserving system for which $3$ -fold correlations decay exponentially for Lipschitz continuous observables. Suppose that $(M_{k})$ is a sequence…

math.DS2025

On recurrence sets for toral endomorphisms

Zhangnan Hu, Tomas Persson

Let $A$ be a $2 \times 2$ integral matrix with an eigenvalue of modulus strictly less than 1. Let $T$ be the natural endomorphism on the torus $\mathbb{T}^2=\mathbb{R}^2/\mathbb{Z}^…