2014/05/30 by Łukasz Pawelec, Lukasz Pawelec, Pawelec, Lukasz +2
Mathematics · #37B45 #37F35 #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #advanced mathematical theories #math.DS #msc:37B45 #msc:37F35
paper · pdf · doi:10.48550/arxiv.1405.7784
arxiv created 2014/05/30 · openalex publication_date 2014/05/30 · arxiv updated 2014/06/02 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We study some forward invariant sets appearing in the dynamics of the exponential family. We prove that the Hausdorff dimension of the sets under consideration is not larger than 1. This allows us to prove, as a consequence, a result for some dynamically defined indecomposable continua which appear in the dynamics of the exponential family. We prove that the Hausdorff dimension of these continua is equal to one.