Continuity of fractal dimensions in conservative generic Markov and Lagrange dynamical spectra

Davi Lima, Carlos Gustavo Moreira, Christian Camilo Silva Villamil

Let ${\phi }_0$ be a smooth conservative diffeomorphism of a compact surface $S$ and let ${\Lambda }_0$ be a transitive horseshoe of ${\phi }_0$. Given a smooth real function $f$ defined in $S$ and a s…