dc.contributor.author | Giza, Robert | |
dc.contributor.author | Morales, Rafael | |
dc.contributor.author | Rock, John A. | |
dc.contributor.author | Knox, Christina | |
dc.contributor.author | Kurianski, Kristin M | |
dc.date.accessioned | 2017-06-20T18:36:13Z | |
dc.date.available | 2017-06-20T18:36:13Z | |
dc.date.issued | 2017-04 | |
dc.identifier.issn | 1937-1632 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/110078 | |
dc.description.abstract | The theory of complex dimensions of fractal strings developed by Lapidus and van Frankenhuijsen has proven to be a powerful tool for the study of Minkowski measurability of fractal subsets of the real line. In a very general setting, the Minkowski measurability of such sets is characterized by the structure of corresponding complex dimensions. Also, this tool is particularly effective in the setting of self-similar fractal subsets of R which have been shown to be Minkowski measurable if and only if they are nonlattice. This paper features a survey on the pertinent results of Lapidus and van Frankenhuijsen and a preliminary extension of the theory of complex dimensions to subsets of Euclidean space, with an emphasis on self-similar sets that satisfy various separation conditions. This extension is developed in the context of box-counting measurability, an analog of Minkowski measurability, which is shown to be characterized by complex dimensions under certain mild conditions. | en_US |
dc.description.sponsorship | National Science Foundation (U.S.) (Grant DMS–1247679) | en_US |
dc.language.iso | en_US | |
dc.publisher | American Institute of Mathematical Sciences (AIMS) | en_US |
dc.relation.isversionof | http://dx.doi.org/10.3934/dcdss.2017011 | en_US |
dc.rights | Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. | en_US |
dc.source | American Institute of Mathematical Sciences | en_US |
dc.title | A survey of complex dimensions, measurability, and the lattice/nonlattice dichotomy | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Dettmers, Kristin et al. “A Survey of Complex Dimensions, Measurability, and the Lattice/Nonlattice Dichotomy.” Discrete and Continuous Dynamical Systems - Series S 10.2 (2017): 213–240. | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
dc.contributor.mitauthor | Kurianski, Kristin M | |
dc.relation.journal | Discrete and Continuous Dynamical Systems - Series S | en_US |
dc.eprint.version | Final published version | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dspace.orderedauthors | Dettmers, Kristin; Giza, Robert; Morales, Rafael; Rock, John A.; Knox, Christina | en_US |
dspace.embargo.terms | N | en_US |
dc.identifier.orcid | https://orcid.org/0000-0002-7550-4049 | |
mit.license | PUBLISHER_POLICY | en_US |