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- Mostapha Benhenda, Elvis Barakovic
- 2012

Let M be a smooth compact connected manifold, on which there exists an effective smooth circle action S t preserving a positive smooth volume. We show that on M, the smooth closure of the smooth volume-preserving conjugation class of some Liouville rotations S α of angle α contains a smooth volume-preserving diffeomorphism T that is metrically isomorphic to… (More)

Let M be a smooth compact connected manifold, on which there exists an effective smooth circle action preserving a positive smooth volume. On M, we construct volume-preserving diffeomorphisms that are metrically isomorphic to ergodic translations on the torus, translations in which one given coordinate of the translation is an arbitrary Liouville number. To… (More)

A celebrated theorem by Herman and Yoccoz asserts that if the rotation number α of a C∞-diffeomorphism of the circle f satisfies a Diophantine condition, then f is C∞-conjugated to a rotation. In this paper, we establish explicit relationships between the Ck norms of this conjugacy and the Diophantine condition on α. To obtain these estimates, we follow a… (More)

- Mostapha Benhenda
- Social Choice and Welfare
- 2011

In this article, we present a model of deliberation based on Rawls’s political liberalism. Our formalization gives a new perspective on his political theory. Moreover, we obtain quantitative results on political deliberation under Rawlsian rules. Finally, we elaborate two arguments in favor of Rawlsian deliberation: first, deliberation is epistemically… (More)

We construct a smooth Gaussian-Kronecker diffeomorphism T , on × [0, 1], where [0, 1] is the Hilbert cube. To obtain this diffeomorphism, we adapt a construction by De La Rue [6], which uses transformations of the planar Brownian motion.

- Mostapha Benhenda
- ArXiv
- 2017

Generating molecules with desired chemical properties is important for drug discovery. The use of generative neural networks is promising for this task. However, from visual inspection, it often appears that generated samples lack diversity. In this paper, we quantify internal chemical diversity, and we raise the following challenge: can a nontrivial AI… (More)

We construct an uncountable family of smooth ergodic zero-entropy diffeomorphisms that are pairwise non-Kakutani equivalent, on any smooth compact connected manifold of dimension greater than two, on which there exists an effective smooth circle action preserving a positive smooth volume. To that end, we first construct a smooth ergodic zero-entropy and… (More)

In this article, we show two related results on circle diffeomorphisms. The first result is on quasi-reducibility: for a Baire-dense set of α, for any diffeomorphism f of rotation number α, it is possible to accumulate Rα with a sequence hn f h−1 n , hn being a diffeomorphism. The second result is: for a Baire-dense set of α, given two commuting… (More)

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