Continuity of Hausdorff dimension across generic dynamical Lagrange and Markov spectra

Aline Cerqueira, Carlos Matheus, Carlos Gustavo Moreira

Let ${\phi }_0$ be a smooth area-preserving diffeomorphism of a compact surface $M$ and let ${\Lambda }_0$ be a horseshoe of ${\phi }_0$ with Hausdorff dimension strictly smaller than one. Given a smoo…