Dimension of the intersection of certain Cantor sets in the plane

• Autorzy: Pedersen Steen , Staw Vincent T.

Identyfikatory

DOI

10.7494/OpMath.2021.41.2.227

• Języki publikacji: EN

Abstrakty

EN

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

EN

Cantor set; fractal; self-similar; translation; intersection; dimension; Minkowski dimension

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2021
• Tom: Vol. 41, no. 2
• Strony: 227--244
• Opis fizyczny: Bibliogr. 35 poz.

Twórcy

autor

Pedersen Steen

• Wright State University Department of Mathematics 3640 Col Glenn Hwy, Dayton, OH 45435, USA

autor

Staw Vincent T.

• Wright State University Department of Mathematics 3640 Col Glenn Hwy, Dayton, OH 45435, USA

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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).