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Quantitative theory reveals recurrence behaviors in piecewise linear maps, suggesting implications for higher dimensions.
Let , and let be an expanding piecewise linear map sending each interval of linearity to [0,1]. For , , and , we consider the recurrence counting function We show that for any we have for ‐almost all and for all , where . We also prove a generalization of this result to higher dimensions.
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Levesley et al. (2025) studied this question.
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