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dc.contributor.authorEceizabarrena D.en_US
dc.date.accessioned2020-03-04T14:02:24Z
dc.date.available2020-03-04T14:02:24Z
dc.date.issued2020-06
dc.identifier.urihttp://hdl.handle.net/20.500.11824/1096
dc.description.abstractRiemann’s non-differentiable function is a classic example of a continuous function which is almost nowhere differentiable, and many results concerning its analytic regularity have been shown so far. However, it can also be given a geometric interpretation, so questions on its geometric regularity arise. This point of view is developed in the context of the evolution of vortex filaments, modelled by the Vortex Filament Equation or the binormal flow, in which a generalisation of Riemann’s function to the complex plane can be regarded as the trajectory of a particle. The objective of this document is to show that the trajectory represented by its image does not have a tangent anywhere. For that, we discuss several concepts of tangent vectors in view of the set’s irregularity.en_US
dc.description.sponsorshipMinisterio de Educación, Cultura y Deporte - FPU15/03078en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.publisherAdvances in Mathematicsen_US
dc.relationinfo:eu-repo/grantAgreement/EC/H2020/669689en_US
dc.relationES/1PE/SEV-2017-0718en_US
dc.relationEUS/BERC/BERC.2018-2021en_US
dc.rightsinfo:eu-repo/semantics/embargoedAccessen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectRiemann’s non-differentiable function, vortex filament, trajectory, fractal, tangent vectorsen_US
dc.titleGeometric differentiability of Riemann's non-differentiable functionen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.typeinfo:eu-repo/semantics/publishedVersionen_US
dc.identifier.arxiv1910.02536
dc.identifier.doi10.1016/j.aim.2020.107091
dc.relation.publisherversionhttps://doi.org/10.1016/j.aim.2020.107091en_US


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