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Some interactions between number theory and multifractal analysis
Virtualconference
Authors : Martin, Bruno (Author of the conference)
CIRM (Publisher )
11A55 - Continued fractions, {For approximation results, See 11J70; See also 11K50, 30B70, 40A15}
26A15 - "Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.), {For properties determined by Fourier coefficients, See 42A16; for those determined by approximation properties, See 41A25, 41A27}"
26A30 - Singular functions, Cantor functions, functions with other special properties
28A80 - Fractals
CIRM (Publisher )
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Abstract :
Some number-theoretic problems have led to the study of some infinite series that show multifractal behaviour, which means that their Hölder pointwise regularity may widely change from point to point. Reviewing some examples such as lacunary trigonometric series, Davenport series, Brjuno-type functions, I will put emphasis on the methods encountered in the literature to compute the pointwise Hölder exponent of such functions.
Keywords : irrationality exponent; Hölder exponent; wavelets; functional equations
MSC Codes : Keywords : irrationality exponent; Hölder exponent; wavelets; functional equations
11A55 - Continued fractions, {For approximation results, See 11J70; See also 11K50, 30B70, 40A15}
26A15 - "Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.), {For properties determined by Fourier coefficients, See 42A16; for those determined by approximation properties, See 41A25, 41A27}"
26A30 - Singular functions, Cantor functions, functions with other special properties
28A80 - Fractals
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 01/12/2020 Conference Date : 24/11/2020 Subseries : Research talks arXiv category : Number Theory ; Dynamical Systems Mathematical Area(s) : Analysis and its Applications ; Number Theory Format : MP4 (.mp4) - HD Video Time : 00:53:28 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2020-11-24_Martin.mp4 
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Information on the Event
Event Title : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoireEvent Organizers : Rivat, Joël ; Tichy, Robert Dates : 23/11/2020 - 27/11/2020 Event Year : 2020 Event URL : https://www.chairejeanmorlet.com/2256.html
Citation Data
DOI : 10.24350/CIRM.V.19688003Cite this video as: Martin, Bruno (2020). Some interactions between number theory and multifractal analysis. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19688003 URI : http://dx.doi.org/10.24350/CIRM.V.19688003 |
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Bibliography
