C. Villamil

activity

20242026

collaborators

5 papers

math.DS2026

Dynamical spectra for skew products with unit circle fiber

Christian Camilo Silva Villamil, Carlos Gustavo Tamm de Araujo Moreira, RaÃºl Mario Ures de la Madrid

The dynamical Markov and Lagrange spectra are subsets of the real line widely studied and that share some similarities with the classical spectra, e.g. typical dynamical spectra, a…

math.DS2026

On the discontinuities of Hausdorff dimension in generic dynamical Lagrange spectrum

Christian Camilo Silva Villamil

Let $I ¨ _{0}$ be a $C^{2}$ -conservative diffeomorphism of a compact surface $S$ and let $I^_{0}$ be a mixing horseshoe of $I ¨ _{0}$ . Given a smooth real function $f$ defined in $S$ and some…

math.DS2025

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

Davi Lima, Carlos Gustavo Moreira, Christian Camilo Silva Villamil

Let $I ¨ _{0}$ be a smooth conservative diffeomorphism of a compact surface $S$ and let $I^_{0}$ be a transitive horseshoe of $I ¨ _{0}$ . Given a smooth real function $f$ defined in $S$ and…

math.DS2025

Hausdorff dimension of some subsets of the Lagrange and Markov spectra near $3$

Christian Camilo Silva Villamil, Carlos Gustavo Moreira

We study the sets $L$ and $M ∖ L$ near $3$ , where $L$ and $M$ are the classical Lagrange and Markov spectra. More specifical…

math.DS2024

Concentration of dimension in the Lagrange spectrum