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)
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)
We construct an uncountable family of smooth ergodic zero-entropy diffeo-morphisms 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)
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 , which uses transformations of the planar Brownian motion.
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 C k norms of this conjugacy and the Diophantine condition on α. To obtain these estimates, we follow… (More)