Talk:Rotation theory

From Scholarpedia
Jump to: navigation, search

    This is an excellent and accurate survey of an interesting and important area of Dynamical Systems written by one of the international leaders in the field.

    I think it would be stronger as an encyclopedia article if it moved beyond the work of the author and his collaborators.

    The title of the article is terminology I have never seen used for the actual content of the article.

    In my opinion the main advance in "rotation theory" after Poincar\'e was Schwarzman's notion of asymptotic cycles which measure the rate of rotation of orbits on a manifold using first homology with real coefficients. This notion was further developed on the topological side and connected to subshifts of finite type, including some of the results credited to Ziemann here, by Fried in the 80's. Ruelle and Sullivan generalized Schwarzman's notion to geometric currents and their connection to hyperbolic dynamics and foliation theory.


    I added 3 sections and made changes in 2 others. Michal Misiurewicz

    Personal tools

    Focal areas