2025/02/18 by Vanderlei Horita, Horita, Vanderlei, Oyran Rayzzaro +1
Mathematics · #37B40 #37C20 #37D30 #37J10 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2502.12812
openalex publication_date 2025/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We investigate the continuity of Hausdorff dimension and box dimension (limit capacity) of non-hyperbolic repellers of diffeomorphisms derived from transitive Anosov diffeomophisms through a Hopf bifurcation studied by Horita and Viana (see Discret. Contin. Dyn. Syst., 13 (2005), 1125-1137). Here, we extend their work showing that both dimensions are continuous at paremeter bifurcation. In the proof, we consider maps with holes introduced by Horita and Viana in Journal of Statistical Physics 105(2001), 835-862 and further developed by Dysman in Journal of Statistical Physics 120(2005),479-509, relating the Hausdorff dimension with the volume of the hole.