2005/01/14 by Benoit Cadre, Benoı̂t Cadre, Cadre, Benoit +2
Mathematics · #37A05 #37A25 #37A35 #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #math.DS #msc:37A05 #msc:37A25 #msc:37A35
paper · pdf · doi:10.48550/arxiv.math/0501222
arxiv created 2005/01/14 · openalex publication_date 2005/01/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define the concept of symmetric sensitivity with respect to initial conditions for the endomorphisms on Lebesgue metric spaces. The idea is that the orbits of almost every pair of nearby initial points (for the product of the invariant measure) of a symmetrically sensitive map may diverge from a positive quantity independent of the initial points. We study the relationships between symmetric sensitivity and weak mixing, symmetric sensitivity and positiveness of metric entropy and we compute the largest sensitivity constant.