C. Villamil

activity

20242026

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6 papers · 1 filter

math.DS2026

Dynamical spectra for skew products with unit circle fiber

Christian Camilo Silva Villamil, Carlos Gustavo Tamm de Araujo Moreira, Raúl 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.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

Christian Camilo Silva Villamil

Let $φ$ be a smooth conservative diffeomorphism of a compact surface $S$ and let $Λ$ be a mixing horseshoe of $φ$ . Given a smooth real function $f$ defined on $S$ , we define for po…

math.DS2024

On the discontinuities of Hausdorff dimension in generic dynamical Lagrange spectrum

Christian Camilo Silva Villamil

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

math.DS2023

Concentration of dimension in extremal points of left-half lines in the Lagrange spectrum

Carlos Gustavo Moreira, Christian Camilo Silva Villamil

We prove that for any $η$ that belongs to the closure of the interior of the Markov and Lagrange spectra, the sets $k^{- 1} ((- \infty, η])$ and $k^{- 1} (η)$ , which are the sets of irra…

math.DS2023

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

Davi Lima, Carlos Gustavo Moreira, Christian Camilo Silva Villamil

Let $φ_{0}$ be a smooth conservative diffeomorphism of a compact surface $S$ and let $Λ_{0}$ be a transitive horseshoe of $φ_{0}$ . Given a smooth real function $f$ defined in $S$ and a s…