Dynamical characterization of initial segments of the Markov and Lagrange spectra

2020/10/29 by Lima, Davi, Moreira, Carlos Gustavo
#Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2010.15291

Abstract

We prove that, for every k≥ 4, the sets M(k) and L(k), which are Markov and Lagrange dynamical spectra related to conservative horseshoes and associated to continued fractions with coefficients bounded by k coincide with the intersections of the classical Markov and Lagrange spectra with (-∞, √(k²+4k)]. We also observe that, despite the corresponding statement is also true for k = 2, it is false for k = 3.

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