Shrinking Targets For IETS: Extending a Theorem of Kurzweil |
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| Authors: | Jon Chaika |
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| Institution: | 1. Department of Mathematics, 5734 S. University Avenue, Chicago, IL, 60637, USA
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| Abstract: | Given an IET T : 0, 1) → 0, 1) and decreasing sequence of positive real numbers with divergent sum a = {ai}￥i=1{{\bf a} = \{a_i\}^\infty_{i=1}} we consider
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ST (a) = {(x, y) ? 0, 1) ×0, 1) : y ? B(Ti x, ai) for infinitely many i }S_T ({\bf a}) = \{(x, y) \in 0, 1) \times 0, 1) : y \in B(T^i x, a_i) \, {\rm for\,infinitely\,many}\,i \} |
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