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Characterizing rational maps positively using graphs

De Dylan Thurston

Apparaît dans la collection : Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe

We can conveniently represent post-critically finite topological branched selfcovers of the sphere to itself using maps of graphs. With this representation, there is also a positive characterization of hyperbolic rational maps among these topological branched self-covers, using energies that control elastic 'stretchiness'. In broad terms, a map is rational iff a network of elastic bands gets looser and looser as you pull it back. This complements the older negative characterization of W. Thurston.

Informations sur la vidéo

Date de captation 21/09/2021
Date de publication 02/11/2021
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19815703
Citer cette vidéo Thurston, Dylan (21/09/2021). Characterizing rational maps positively using graphs . CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19815703
URL https://dx.doi.org/10.24350/CIRM.V.19815703

Domaine(s)

Bibliographie

THURSTON, Dylan P. A positive characterization of rational maps. Annals of Mathematics, 2020, vol. 192, no 1, p. 1-46. - https://doi.org/10.4007/annals.2020.192.1.1
THURSTON, Dylan P. From rubber bands to rational maps: a research report. Research in the Mathematical Sciences, 2016, vol. 3, no 1, p. 1-49. - https://doi.org/10.1186/s40687-015-0039-4

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