arXiv subjects

Alberto Sarmiento

Publications and source records attributed to Alberto Sarmiento.

3 recordsLinked to original sources

arXiv2026

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

We establish a complete structural classification for continuum-wise hyperbolic surface homeomorphisms. Specifically, we prove that a surface homeomorphism is cw$_F$-hyperbolic if, and only if, it is a pseudo-Anosov homeomorphism whose singularities consist exclusively of spines (1-prongs). Furthermore, we classify these systems up to topological conjugacy, showing that every such homeomorphism is conjugate to either an Anosov automorphism on the torus $\mathbb{T}^2$ or to its standard hyperelliptic quotient on the sphere $\mathbb{S}^2$. As a rigid consequence of this classification, we show that such dynamics are strictly obstructed on surfaces of genus greater than one, the Klein bottle, and the projective plane.

math.DS↗

arXiv2025

Anomalous cw-expansive homeomorphisms on compact surfaces of higher genus

In this paper, we construct cw-expansive homeomorphisms on compact surfaces of genus greater than or equal to zero with a fixed point whose local stable set is connected but not locally connected. This provides an affirmative answer to question posed by Artigue [3]. To achieve this, we generalize the construction from the example of Artigue, Pacifico and Vieitez [6], obtaining examples of homeomorphisms on compact surfaces of genus greater than or equal to two that are 2-expansive but not expansive. On the sphere and the torus, we construct new examples of cw2-expansive homeomorphisms that are not N -expansive for all N greater than or equal to one.

math.DS↗

arXiv2023

Continuum-wise hyperbolic homeomorphisms on surfaces

This paper discusses the dynamics of continuum-wise hyperbolic surface homeomorphisms. We prove that $cw_F$-hyperbolic surface homeomorphisms containing only a finite set of spines are $cw_2$-hyperbolic. In the case of $cw_3$-hyperbolic homeomorphisms we prove the finiteness of spines and, hence, that $cw_3$-hyperbolicity implies $cw_2$-hyperbolicity. In the proof, we adapt techniques of Hiraide [11] and Lewowicz [15] in the case of expansive surface homeomorphisms to prove that local stable/unstable continua of $cw_F$-hyperbolic homeomorphisms are continuous arcs. We also adapt techniques of Artigue, Pac\'ifico and Vieitez [6] in the case of N-expansive surface homeomorphisms to prove that the existence of spines is strongly related to the existence of bi-asymptotic sectors and conclude that spines are necessarily isolated from other spines.

math.DS↗