Intrinsic Ergodicity of Open dynamical systems for the doubling map

2015/09/01 by Rafael Alcaraz Barrera, Barrera, Rafael Alcaraz
Computer Science · Mathematics · #28D05 #37B10 #37C70. 37E05 #68R15 #Advanced Differential Equations and Dynamical Systems #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.DS #msc:28D05 #msc:37B10 #msc:37C70. #msc:37E05 #msc:68R15

paper · pdf · doi:10.48550/arxiv.1509.00255

26 pages. This paper continues the work started in arXiv.org > math > arXiv:1506.00067

arxiv created 2015/09/01 · openalex publication_date 2015/09/01 · arxiv updated 2015/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give sufficient conditions for intervals (a,b) such that the associated open dynamical system for the doubling map is intrinsically ergodic. We also show that the set of parameters (a,b) ∈ ((1)/(4), (1)/(2)) × ((1)/(2),(3)/(4)) such that the attractor (Λ_(a,b), f_(a,b)) is intrinsically ergodic has full Lebesgue measure and we construct a set of points where intrinsic ergodicity does not hold.

Citations

• Topological dynamics of the doubling map with asymmetrical holes

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