2023/02/22 by Douglas Coates, Coates, Douglas, Stefano Luzzatto +1
Computer Science · Mathematics · #37A10 #37C40 #37C83 #37E05 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2302.11411
openalex publication_date 2023/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a class \widehat\mathfrakF of one-dimensional full branch maps introduced in [Doubly Intermittent Full Branch Maps with Critical Points and Singularities; D. Coates, S. Luzzatto, M. Mubarak, 2022], admitting two indifferent fixed points as well as critical points and/or singularities with unbounded derivative. We show that \widehat\mathfrakF can be partitioned into 3 pairwise disjoint subfamilies \widehat\mathfrakF = \mathfrakF ∪ \mathfrakF_± ∪ \mathfrakF_* such that all g ∈ \mathfrakF have a unique physical measure equivalent to Lebesgue, all g ∈ \mathfrakF± have a physical measure which is a Dirac-δ measure on one of the (repelling) fixed points, and all g ∈ \mathfrakF* are non-statistical and in particular have no physical measure. Moreover we show that these subfamilies are intermingled: they can all be approximated by maps in the other subfamilies in natural topologies.