2024/09/09 by O'Hare, Thomas Aloysius · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2409.05857
openalex publication_date 2024/09/09 · openalex created_date 2024/10/21 · openalex updated_date 2026/07/28
Let f,g be C2 area-preserving Anosov diffeomorphisms on \mathbbT2 which are topologically conjugate by a homeomorphism h (hf=gh). We assume that the Jacobian periodic data of f and g are matched by h for all points of some large period N∈ℕ. We show that f and g are ``approximately smoothly conjugate." That is, there exists a C1+α diffeomorphism hN such that h and hN are C0 exponentially close in N, and f and fN:=hN-1ghN are C1 exponentially close in N. Moreover, the rates of convergence are uniform among different f,g in a C2 bounded set of Anosov diffeomorphisms. The main idea in constructing hN is to do a ``weighted holonomy" construction, and the main technical tool in obtaining our estimates is a uniform effective version of Bowen's equidistribution theorem of weighted discrete orbits to the SRB measure.