Box-counting by Hölder's traveling salesman

Balogh, Zoltán M.; Züst, Roger (2020). Box-counting by Hölder's traveling salesman. Archiv der Mathematik, 114(5), pp. 561-572. Birkhäuser 10.1007/s00013-019-01415-5

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We provide a sufficient Dini-type condition for a subset of a complete, quasiconvex metric space to be covered by a Hölder curve. This implies in particular that if the upper box-counting dimension is less than d≥1, then it can be covered by an 1/d-Hölder curve. On the other hand, for each 1≤d<2 we give an example of a compact set in the plane with lower box-counting dimension equal to zero and upper box-counting dimension equal to d, just failing the above Dini-type condition, that can not be covered by a countable collection of 1/d-Hölder curves.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Balogh, Zoltan and Züst, Roger

Subjects:

500 Science > 510 Mathematics

ISSN:

0003-889X

Publisher:

Birkhäuser

Funders:

[4] Swiss National Science Foundation

Language:

English

Submitter:

Sebastiano Don

Date Deposited:

28 Jan 2021 17:59

Last Modified:

28 Jan 2021 17:59

Publisher DOI:

10.1007/s00013-019-01415-5

ArXiv ID:

1907.05227

Uncontrolled Keywords:

Hausdorff dimension, Box-counting dimension, Fractals, Hölder maps

BORIS DOI:

10.48350/151223

URI:

https://boris.unibe.ch/id/eprint/151223

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