Quantitative recurrence properties for self-conformal sets
نویسندگان
چکیده
In this paper we study the quantitative recurrence properties of self-conformal sets X X equipped with map T colon upper X right-arrow T : ? encoding="application/x-tex">T:X\to X induced by left shift. particular, given a function alttext="phi double-struck N left-parenthesis 0 comma normal infinity right-parenthesis comma"> ? N stretchy="false">( 0 , mathvariant="normal">?<!-- ? stretchy="false">) encoding="application/x-tex">\varphi :\mathbb {N}\to (0,\infty ), metric set R = { x ?<!-- ? stretchy="false">| n ?<!-- ? <mml:mo>> } . encoding="application/x-tex">\begin{equation*} R(T,\varphi )=\left \{x\in X:|T^nx-x|>\varphi (n)\text { }n\in \mathbb {N}\right \}. \end{equation*} Our main result shows that natural measure supported on , right-parenthesis"> encoding="application/x-tex">R(T,\varphi ) has zero if volume sum converges, and under open condition full diverges.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2021
ISSN: ['2330-1511']
DOI: https://doi.org/10.1090/proc/15285