Diffusion limit for a slow-fast standard map | Vidéo | Carmin.tv

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Diffusion limit for a slow-fast standard map

By Jacopo De Simoi

Appears in collection : Probabilistic limit theorems for dynamical systems / Théorèmes limites probabilistes pour les systèmes dynamiques

Consider the map $(x, z) \mapsto (x + \epsilon^{-\alpha} \sin (2\pi x) + \epsilon^{-(1+\alpha)}z, z + \epsilon \sin(2\pi x))$, which is conjugate to the Chirikov standard map with a large parameter. For suitable $\alpha$, we obtain a central limit theorem for the slow variable $z$ for a (Lebesgue) random initial condition. The result is proved by conjugating to the Chirikov standard map and utilizing the formalism of standard pairs. Our techniques also yield for the Chirikov standard map a related limit theorem and a ''finite-time'' decay of correlations result. This is joint work with Alex Blumenthal and Ke Zhang.

Information about the video

Date of recording 31/10/2018
Date of publication 08/11/2018
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19471703
Cite this video De Simoi, Jacopo (31/10/2018). Diffusion limit for a slow-fast standard map. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19471703
URL https://dx.doi.org/10.24350/CIRM.V.19471703

Domain(s)

Dynamical Systems

Bibliography

Blumenthal, A., De Simoi, J., & Zhang, K. (2018). Diffusion limit for a slow-fast standard map. <arXiv:1806.06398> - https://arxiv.org/abs/1806.06398

MSC codes

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