Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
In this paper we consider a retained digits Cantor set T based on digit expansions with Gaussian integer base. Let F be the set all x such that the intersection of T with its translate by x is non-empty and let Fβ be the subset of F consisting of all x such that the dimension of the intersection of T with its translate by x is β times the dimension of T. We find conditions on the retained digits sets under which Fβ is dense in F for all 0 ≤ β ≤ 1. The main novelty in this paper is that multiplication the Gaussian integer base corresponds to an irrational (in fact transcendental) rotation in the complex plane.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
227--244
Opis fizyczny
Bibliogr. 35 poz.
Twórcy
autor
- Wright State University Department of Mathematics 3640 Col Glenn Hwy, Dayton, OH 45435, USA
autor
- Wright State University Department of Mathematics 3640 Col Glenn Hwy, Dayton, OH 45435, USA
Bibliografia
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Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f1366c17-1964-4910-9ee5-7316520e716b