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Conformal measures and currents in holomorphic dynamics
Multi angle
Authors : Lyubich, Mikhail (Author of the conference)
CIRM (Publisher )
14L30 - Group actions on varieties or schemes (quotients)
22E40 - Discrete subgroups of Lie groups
37F10 - Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37F35 - Conformal densities and Hausdorff dimension
57S25 - Groups acting on specific manifolds
32U40 - Currents
CIRM (Publisher )
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Abstract :
We will overview notions of conformal measures and currents, and a Patterson-Sullivan method of constructing them, in various branches of Holomorphic Dynamics: for 1D rational maps and their natural extensions, complex Henon maps and classical Kleinian group, with an eye towards an extension to higher rank actions.
Keywords : conformal measures and currents; Patterson-Sullivan method; Henon maps; algebraic groups actions; flag manifolds
MSC Codes : Keywords : conformal measures and currents; Patterson-Sullivan method; Henon maps; algebraic groups actions; flag manifolds
14L30 - Group actions on varieties or schemes (quotients)
22E40 - Discrete subgroups of Lie groups
37F10 - Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37F35 - Conformal densities and Hausdorff dimension
57S25 - Groups acting on specific manifolds
32U40 - Currents
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 31/07/2025 Conference Date : 08/07/2025 Subseries : Research talks arXiv category : Complex Variables ; Dynamical Systems Mathematical Area(s) : Analysis and its Applications ; Dynamical Systems & ODE Format : MP4 (.mp4) - HD Video Time : 01:04:18 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-07-08_Lyubich.mp4 
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Information on the Event
Event Title : Complex Geometry, Complex Analysis and Dynamics / Géométrie Complexe, Analyse et Dynamique ComplexeEvent Organizers : Biard, Séverine ; Dinh, Tien-Cuong ; Ma, Xiaonan ; Marinescu, George Dates : 07/07/2025 - 11/07/2025 Event Year : 2025 Event URL : https://conferences.cirm-math.fr/3351.html
Citation Data
DOI : 10.24350/CIRM.V.20369103Cite this video as: Lyubich, Mikhail (2025). Conformal measures and currents in holomorphic dynamics. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20369103 URI : http://dx.doi.org/10.24350/CIRM.V.20369103 |
See Also
- [Multi angle] Perturbations of parabolic endomorphisms in dimension 2 / Author of the conference Raissy, Jasmin.
- [Multi angle] On K3 surfaces with non-elementary hyperbolic automorphism group / Author of the conference Oguiso, Keiji.
- [Multi angle] Starting with the Gauss-Bonnet formula: rigidity phenomena on bounded symmetric domains / Author of the conference Mok, Ngaiming.
- [Multi angle] Holomorphic symplectic geometry of elliptic surfaces / Author of the conference Hwang, Jun-Muk.
Bibliography
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