Critical curves of rotations

2023/03/31 by Roberts, John A G, Saito, Asaki, Vivaldi, Franco
#37E10 (Primary) 37B10 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.17955

Abstract

In rotations with a binary symbolic dynamics, a critical curve is the locus of parameters for which the boundaries of the partition that defines the symbolic dynamics are connected via a prescribed number of iterations and symbolic itinerary. We study the arithmetical and geometrical properties of these curves in parameter space.

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