On the Lagrange and Markov Dynamical Spectra

2013/10/15 by Sergio Augusto Romaña Ibarra, Ibarra, Sergio Augusto Romaña, Carlos Gustavo T. de A. Moreira +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1310.3903

arxiv created 2015/05/19 · arxiv updated 2015/05/20

Abstract

We consider the Lagrange and the Markov dynamical spectra associated to horseshoes on surface with Hausdorff dimensions greater than 1. We show that for a "large" set of real functions on the surface and for "typical" horseshoes with Hausdorff dimensions greater than 1, then both the Lagrange and the Markov dynamical spectrum have persistently non-empty interior.

Related

• On the minima of Markov and Lagrange Dynamical Spectra
• Continuity of Hausdorff dimension across generic dynamical Lagrange and Markov spectra
• Continuity of fractal dimensions in conservative generic Markov and Lagrange dynamical spectra
• Dynamical characterization of initial segments of the Markov and Lagrange spectra
• Phase Transitions on the Markov and Lagrange Dynamical Spectra