2014/03/06 by Gregory R. Conner, Conner, Gregory R., Wolfram Hojka +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #20F69) #20M05 #20M20 (37B45 #37B10 #37C70 #54D05 #Caveolin-1 and cellular processes #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:20M05 #msc:20M20 #msc:37B10 #msc:37C70 #msc:54D05
paper · pdf · doi:10.48550/arxiv.1403.1516
arxiv created 2014/03/06 · openalex publication_date 2014/03/06 · arxiv updated 2014/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Guided by classical concepts, we define the notion of ends of an iterated function system and prove that the number of ends is an upper bound for the number of nondegenerate components of its attractor. The remaining isolated points are then linked to idempotent maps. A commutative diagram illustrates the natural relationships between the infinite walks in a semigroup and components of an attractor in more detail. We show in particular that, if an iterated function system is one-ended, the associated attractor is connected, and ask whether every connected attractor (fractal) conversely admits a one-ended system.