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Central limit theorems for circle packings
Multi angle
Authors : Pollicott, Mark (Author of the conference)
CIRM (Publisher )
11K55 - Metric theory of other number-theoretic algorithms and expansions
37C30 - Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems
37D35 - Thermodynamic formalism, variational principles, equilibrium states
37F35 - Conformal densities and Hausdorff dimension
52C26 - Circle packings and discrete conformal geometry
CIRM (Publisher )
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Abstract :
Given the Apollonian Circle packing, or something similar, one can consider the distribution of the logarithms of the radii. These can be shown to satisfy a Central Limit Theorem. The method of proof uses iterated function schemes and transfer operators and has applications to other conformal dynamical systems.
MSC Codes : 11K55 - Metric theory of other number-theoretic algorithms and expansions
37C30 - Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems
37D35 - Thermodynamic formalism, variational principles, equilibrium states
37F35 - Conformal densities and Hausdorff dimension
52C26 - Circle packings and discrete conformal geometry
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 03/03/17 Conference Date : 21/02/17 Subseries : Research talks arXiv category : Dynamical Systems ; Differential Geometry ; Number Theory Mathematical Area(s) : Dynamical Systems & ODE ; Geometry ; Number Theory Format : MP4 (.mp4) - HD Video Time : 00:55:54 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-02-21_Pollicott.mp4 
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Information on the Event
Event Title : Non uniformly hyperbolic dynamical systems. Coupling and renewal theory / Systèmes dynamiques non uniformement et partiellement hyperboliques. Couplage, renouvellementEvent Organizers : Troubetzkoy, Serge ; Vaienti, Sandro Dates : 20/02/17 - 24/02/17 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1714.html
Citation Data
DOI : 10.24350/CIRM.V.19128903Cite this video as: Pollicott, Mark (2017). Central limit theorems for circle packings. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19128903 URI : http://dx.doi.org/10.24350/CIRM.V.19128903 |
See Also
- [Multi angle] Fast-Slow partially hyperbolic systems: an example / Author of the conference Liverani, Carlangelo.
- [Multi angle] Mixing and rates of mixing for infinite measure flows / Author of the conference Melbourne, Ian.
- [Multi angle] Generic properties of the geodesic flow in nonpositive curvature / Author of the conference Coudène, Yves.
- [Post-edited] Singular hyperbolicity and homoclinic tangencies of 3-dimensional flows / Author of the conference Crovisier, Sylvain.
Bibliography
- Pollicott, M. (2015). Apollonian circle packings. In C. Bandt, K. Falconer, & M. Zähle (Eds.), Fractal geometry and stochastics V (pp. 121-142). Cham: Birkhäuser - http://dx.doi.org/10.1007/978-3-319-18660-3_8
