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pro vyhledávání: '"Fougeron, Charles"'
We obtain expansions of ergodic integrals for $\Z^d$-covers of compact self-similar translation flows, and as a consequence we obtain a form of weak rational ergodicity with optimal rates. As examples, we consider the so-called self-similar $(s,1)$-s
Externí odkaz:
http://arxiv.org/abs/2402.02266
Autor:
Filip, Simion, Fougeron, Charles
We exhibit an infinite family of discrete subgroups of ${Sp}_4(\mathbb R)$ which have a number of remarkable properties. Our results are established by showing that each group plays ping-pong on an appropriate set of cones. The groups arise as the mo
Externí odkaz:
http://arxiv.org/abs/2106.09181
We introduce a new renormalization procedure on double rotations, which is reminiscent of the classical Rauzy induction. Using this renormalization we prove that the set of parameters which induce infinite type double rotations has Hausdorff dimensio
Externí odkaz:
http://arxiv.org/abs/2102.11803
Autor:
Fougeron, Charles
We propose a new point of view on multidimensional continued fraction algorithms inspired by Rauzy induction. The generic behaviour of such an algorithm is described here as a random walk on a graph that we call simplicial system. These systems provi
Externí odkaz:
http://arxiv.org/abs/2001.01367
In the current paper we prove simplicity for the spectrum of Lyapunov exponents for triangle sequence and Selmer algorithm in dimension 3. We introduce a strategy that can be applied for a wide class of Markovian MCF.
Externí odkaz:
http://arxiv.org/abs/1904.13297
Autor:
Fougeron, Charles
Cette thèse est articulée autour de deux thématiques : la première (chapitres 1 à 3) est l’étude des exposants de Lyapunov associés à un fibré plat sur une courbe complexe, et en particulier leur application dans les modèles de wind-tree
Externí odkaz:
http://www.theses.fr/2017USPCC160/document
Autor:
Fougeron, Charles
Consider a windtree model with several parallel arbitrary right-angled obstacles placed periodically on the plane. We show that its diffusion rate is the largest Lyapunov exponent of some stratum of quadratic differentials and exhibit a new general s
Externí odkaz:
http://arxiv.org/abs/1803.10717
Autor:
Fougeron, Charles
Consider the flat bundle on $\mathrm{CP}^1 - \{0,1,\infty \}$ corresponding to solutions of the hypergeometric differential equation $ \prod_{i=1}^h (\mathrm D - \alpha_i) - z \prod_{j=1}^h (\mathrm D - \beta_j) = 0$ where $\mathrm D = z \frac {d}{dz
Externí odkaz:
http://arxiv.org/abs/1701.08387
Publikováno v:
Ergod. Th. Dynam. Sys. 40 (2020) 2073-2097
We describe in this article the dynamics of a $1$-parameter family of affine interval exchange transformations. It amounts to studying the directional foliations of a particular affine surface, the Disco surface. We show that this family displays var
Externí odkaz:
http://arxiv.org/abs/1701.02332
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