T. Persson

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math.DS2024

A parameter ASIP for the quadratic family

Magnus Aspenberg, Viviane Baladi, Tomas Persson

Consider the quadratic family $T_{a} (x) = a x (1 - x)$ , for $x \in [0, 1]$ and mixing Collet--Eckmann (CE) parameters $a \in (2, 4)$ . For bounded $I ¨ $ , set $\tilde Ï_{a} := Ï- \int…

math.DS2024

A strong Borel--Cantelli lemma for recurrence

Tomas Persson

Consider a mixing dynamical systems $([0, 1], T, I^¼)$ , for instance a piecewise expanding interval map with a Gibbs measure $I^¼$ . Given a non-summable sequence $(m_{k})$ of non-negati…