Constru tion of urious minimal uniquely ergodi

Niveau: Secondaire, Lycée, Terminale
ar X iv :m at h. D S/ 06 05 43 8 v1 16 M ay 2 00 6 Constru tion of urious minimal uniquely ergodi homeomorphisms on manifolds: the Denjoy-Rees te hnique F. Beguin y , S. Crovisier z and F. Le Roux x 17th May 2006 Abstra t In [23?, Mary Rees has onstru ted a minimal homeomorphism of the 2-torus with pos- itive topologi al entropy. This homeomorphism f is obtained by enri hing the dynami s of an irrational rotation R. We improve Rees onstru tion, allowing to start with any homeomorphism R instead of an irrational rotation and to ontrol pre isely the measurable dynami s of f . This yields in parti ular the following result: Any ompa t manifold of dimension d 2 whi h arries a minimal uniquely ergodi homeomorphism also arries a minimal uniquely ergodi homeomorphism with positive topologi al entropy. More generally, given some homeomorphism R of a ( ompa t) manifold and some home- omorphism h C of a Cantor set, we onstru t a homeomorphism f whi h \looks like R from the topologi al viewpoint and \looks like R h C from the measurable viewpoint.

• topologi al


• ergodi homeomorphisms


• minimal homeomorphism


• minimal uniquely


• constru tion


• ting examples


• stri tly


• tion pro


• measurable dynami