2011/12/27 by Dmitry Ryzhov, Ryzhov, Dmitry
Computer Science · Mathematics · #37A25 #37A50 (Secondary) #37D20 (Primary) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1112.6023
openalex publication_date 2011/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we present an example of C^∞-diffeomorphism of a compact 4-manifold such that it admits a global SRB measure μbut for which the special ergodic theorem doesn't hold. Namely, for this transformation there exist a continuous function ϕand a positive constant αsuch that the following holds: the set of the initial points for which the Birkhoff time averages of the function ϕdiffer from its μ--space average by at least αhas zero Lebesgue measure but full Hausdorff dimension.