B. Carvalho

collaborators

3 papers

math.DS2026

Box dimension of stable sub-slices of fractal graphs over Anosov automorphisms

Bernardo Carvalho, Rafael da Costa Pereira

We consider fractal graphs invariant by a skew product $F : T^{k} \times R \to T^{k} \times R$ of the form $F (x, y) = (A x, I^» y + p (x))$ where $0 < I^» < 1$ …

math.DS2026

Continuum-wise hyperbolicity is exactly the pseudo-Anosov dynamics with spine singularities

Rodrigo Arruda, Bernardo Carvalho, Piotr Oprocha +1

We establish a complete structural classification for continuum-wise hyperbolic surface homeomorphisms. Specifically, we prove that a surface homeomorphism is cw $_{F}$ -hyperbolic if,…

math.DS2026

$C^{1}$ -generic continuum-wise expansive surface diffeomorphisms

We exhibit a local residual set of surface $C^{1}$ diffeomorphisms that are continuum-wise expansive but are not expansive. We also exhibit an open and dense set of surface $C^{1}$ dif…

Box dimension of stable sub-slices of fractal graphs over Anosov automorphisms

Continuum-wise hyperbolicity is exactly the pseudo-Anosov dynamics with spine singularities

C1-generic continuum-wise expansive surface diffeomorphisms

$C^{1}$ -generic continuum-wise expansive surface diffeomorphisms