The Lagrange and Markov spectra from the dynamical point of view

2017/03/06 by Carlos Matheus, Matheus, Carlos
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1703.01748

openalex publication_date 2017/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This text grew out of my lecture notes for a 4-hours minicourse delivered on October 17 & 19, 2016 during the research school "Applications of Ergodic Theory in Number Theory" -- an activity related to the Jean-Molet Chair project of Mariusz Lemańczyk and Sébastien Ferenczi -- realized at CIRM, Marseille, France. The subject of this text is the same of my minicourse, namely, the structure of the so-called Lagrange and Markov spectra (with an special emphasis on a recent theorem of C. G. Moreira).

Related

• Diophantine approximations, Markov and Lagrange spectra and dynamical\n Cantor sets
• Fractal geometry of the complement of Lagrange spectrum in Markov spectrum
• Dynamical characterization of initial segments of the Markov and Lagrange spectra
• Approximation of the Lagrange and Markov spectra
• Markov spectrum near Freiman's isolated points in M∖ L