T. Persson

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math.DS2025

Strong Borel--Cantelli Lemmas for Recurrence

Tomas Persson, Alejandro Rodriguez Sponheimer

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

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}^…

math.DS2024

On shrinking targets for linear expanding and hyperbolic toral endomorphisms

Zhang-nan Hu, Tomas Persson, Wanlou Wu +1

Let $A$ be an invertible $d \times d$ matrix with integer elements. Then $A$ determines a self-map $T$ of the $d$ -dimensional torus $T^{d} = R^{d} / Z^{d}$ . Given a…