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Besov spaces in multifractal environment, and the Frisch-Parisi conjecture
Multi angle
Authors : Seuret, Stéphane (Author of the conference)
CIRM (Publisher )
37F35 - Conformal densities and Hausdorff dimension
CIRM (Publisher )
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Abstract :
Multifractal properties of data coming from many scientific fields (especially in turbulence) are now rigorously established. Unfortunately, the parameters measured on these data do not correspond to those mathematically obtained for the typical (or almost sure) functions in the standard functional spaces: Hölder, Sobolev, Besov…
In this talk, we introduce very natural Besov spaces in which typical functions possess very rich scaling properties, mimicking those observed on data for instance. We obtain various characterizations of these function spaces, in terms of oscillations or wavelet coefficients.
Combining this with the construction of almost-doubling measures with prescribed scaling properties, we are able to bring a solution to the so-called Frisch-Parisi conjecture. This is a joint work with Julien Barral (Université Paris-Nord).
Keywords : Frisch-Parisi conjecture
MSC Codes : In this talk, we introduce very natural Besov spaces in which typical functions possess very rich scaling properties, mimicking those observed on data for instance. We obtain various characterizations of these function spaces, in terms of oscillations or wavelet coefficients.
Combining this with the construction of almost-doubling measures with prescribed scaling properties, we are able to bring a solution to the so-called Frisch-Parisi conjecture. This is a joint work with Julien Barral (Université Paris-Nord).
Keywords : Frisch-Parisi conjecture
37F35 - Conformal densities and Hausdorff dimension
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 23/01/2020 Conference Date : 12/12/2019 Subseries : Research talks arXiv category : Functional Analysis ; Metric Geometry ; Mathematical Physics Mathematical Area(s) : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Video Time : 00:40:30 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-12-12_Seuret.mp4 
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Information on the Event
Event Title : Jean-Morlet Chair 2019 - Conference - Thermodynamic Formalism: Dynamical Systems, Statistical Properties and their Applications / Chaire Jean-Morlet 2019 - Conférence - Formalisme thermodynamique : systèmes dynamiques, propriétés statistiques et leurs applicationsEvent Organizers : Nicol, Matthew ; Pollicott, Mark ; Troubetzkoy, Serge ; Vaienti, Sandro Dates : 09/12/2019 - 13/12/2019 Event Year : 2019 Event URL : https://www.chairejeanmorlet.com/2109.html
Citation Data
DOI : 10.24350/CIRM.V.19586903Cite this video as: Seuret, Stéphane (2019). Besov spaces in multifractal environment, and the Frisch-Parisi conjecture. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19586903 URI : http://dx.doi.org/10.24350/CIRM.V.19586903 |
See Also
- [Multi angle] Marked length spectrum rigidity and the geodesic stretch / Author of the conference Knieper, Gerhard.
- [Multi angle] Intermediate dimensions, capacities and projections / Author of the conference Falconer, Kenneth.
- [Multi angle] Closed geodesics and the measure of maximal entropy on surfaces without conjugate points / Author of the conference Climenhaga, Vaughn.
- [Post-edited] Emergence of wandering stable components / Author of the conference Berger, Pierre.
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