Files in this item
On Hölder solutions to the spiral winding problem
Item metadata
dc.contributor.author | Fraser, Jonathan | |
dc.date.accessioned | 2021-05-13T13:30:12Z | |
dc.date.available | 2021-05-13T13:30:12Z | |
dc.date.issued | 2021-05-07 | |
dc.identifier | 273170241 | |
dc.identifier | 2f01caf1-2637-4106-9346-de083c8c338c | |
dc.identifier | 85107053675 | |
dc.identifier | 000649647600001 | |
dc.identifier.citation | Fraser , J 2021 , ' On Hölder solutions to the spiral winding problem ' , Nonlinearity , vol. 34 , no. 5 , pp. 3251–3270 . https://doi.org/10.1088/1361-6544/abe75e | en |
dc.identifier.issn | 0951-7715 | |
dc.identifier.other | ORCID: /0000-0002-8066-9120/work/90112118 | |
dc.identifier.uri | https://hdl.handle.net/10023/23185 | |
dc.description | The author was supported by an EPSRC Standard Grant No. (EP/R015104/1) and a Leverhulme Trust Research Project Grant No. (RPG-2019-034). | en |
dc.description.abstract | The winding problem concerns understanding the regularity of functions which map a line segment onto a spiral. This problem has relevance in fluid dynamics and conformal welding theory, where spirals arise naturally. Here we interpret 'regularity' in terms of Hölder exponents and establish sharp results for spirals with polynomial winding rates, observing that the sharp Hölder exponent of the forward map and its inverse satisfy a formula reminiscent of Sobolev conjugates. We also investigate the dimension theory of these spirals, in particular, the Assouad dimension, Assouad spectrum and box dimensions. The aim here is to compare the bounds on the Hölder exponents in the winding problem coming directly from knowledge of dimension (and how dimension distorts under Hölder image) with the sharp results. We find that the Assouad spectrum provides the best information, but that even this is not sharp. We also find that the Assouad spectrum is the only 'dimension' which distinguishes between spirals with different polynomial winding rates in the superlinear regime. | |
dc.format.extent | 20 | |
dc.format.extent | 827550 | |
dc.language.iso | eng | |
dc.relation.ispartof | Nonlinearity | en |
dc.subject | Spiral | en |
dc.subject | Winding problem | en |
dc.subject | Holder exponents | en |
dc.subject | Assouad dimension | en |
dc.subject | Box dimension | en |
dc.subject | Assousad spectrum | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | On Hölder solutions to the spiral winding problem | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.sponsor | The Leverhulme Trust | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | 10.1088/1361-6544/abe75e | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | https://arxiv.org/abs/1905.07563 | en |
dc.identifier.grantnumber | EP/R015104/1 | en |
dc.identifier.grantnumber | RPG-2019-034 | en |
This item appears in the following Collection(s)
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.