On weak separation property for self-affine Jordan arcs

2020/06/23 by Andrei Tetenov, Tetenov, Andrei, Olesya Chelkanova +1
Mathematics · Computer Science · Physics and Astronomy · #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2006.13199

Abstract

We consider self-affine arcs in \mathbb R² and prove that violation of "inner" weak separation property for such arcs implies that the arc is a parabolic segment. Therefore, if a self-affine Jordan arc is not a parabolic segment, then it is the attractor of some multizipper.

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