1996 **Abstract:** Explicit formulas are obtained for a family of continuous mappings of p-adic numbers Q p and solenoids T p into the complex plane C and the space R 3 , respectively. Accordingly, this family includes the mappings for which the Cantor set and the Sierpinski triangle are images of the unit balls in Q 2 and Q 3 . In each of the families, the subset of the embeddings is found. For these embeddings, the Hausdorff dimensions are calculated and it is shown that the fractal measure on the image of Q p coincides with t…

Help me understand this report

Search citation statements

Select...

1

1

1

0

3

0

Year Published

2008

2018

Publication Types

Select...

2

1

Relationship

0

3

Authors

Journals

0

3

0

“…One may wish to somehow visualize their action on Z 2 . Recall that the space Z 2 is not Euclidean and totally disconnected, which makes it difficult to represent graphically [8,11]. It is known to be homeomorphic to the Cantor ternary set, which has Lebesgue measure 0.…”

- Search over 1.2b+ citation statments to see what is being said about any topic in the research literature
- Advanced Search to find publications that support or contrast your research
- Citation reports and visualizations to easily see what publications are saying about each other
- Browser extension to see Smart Citations wherever you read research
- Dashboards to evaluate and keep track of groups of publications
- Alerts to stay on top of citations as they happen
- Automated reference checks to make sure you are citing reliable research in your manuscripts
**7 day free preview of our premium features.**

Over 130,000 students researchers, and industry experts at use scite

See what students are saying

“…One may wish to somehow visualize their action on Z 2 . Recall that the space Z 2 is not Euclidean and totally disconnected, which makes it difficult to represent graphically [8,11]. It is known to be homeomorphic to the Cantor ternary set, which has Lebesgue measure 0.…”

“…Another kind of description of the Haar measure on the p-adic integers can also be found in Hewitt and Ross [8, p. 220]. One can find a construction of the Haar measure on the p-adic solenoid in Chistyakov [6,Section 3]. It is based on Hausdorff measures and rather sophisticated, while our simpler construction (Theorem 5.1) is based on a probabilistic method and reflects the structure of the p-adic solenoid.…”

“…In recent years, p-adic analysis has been used in various areas of mathematics as well as in aspects of quantum physics and string theory (Lapidus and van Frankenhuijsen 2006). For a detailed analysis of fractal string and p-adic integers, one may refer to (Chistyakov 1996; Hung 2007; Koblitz 1984; Robert 2000; Schikhof 1984; Vladimirov et al 1994). …”