arXiv subjects

Fábio Armando Tal

Publications and source records attributed to Fábio Armando Tal.

4 recordsLinked to original sources

arXiv2026

Fully chaotic conservative models for some torus homeomorphisms

We study homotopic-to-the-identity torus homeomorphisms, whose rotation set has nonempty interior. We prove that any such map is monotonically semiconjugate to a homeomorphism that preserves the Lebesgue measure, and that has the same rotation set. Furthermore, the dynamics of the quotient map has several interesting chaotic traits: for instance, it is topologically mixing, has a dense set of periodic points and is continuum-wise expansive. In particular, this shows that a convex compact set of $\mathbb{R}^2$ with nonempty interior is the rotation set of the lift of a homeomorphism of $\mathbb{T}^2$ if and only if it is the rotation set of the lift of a conservative homeomorphism.

math.DS↗

arXiv2026

Bounded deviations in higher genus I: closed geodesics

This is the first article of a series of two where we study the problem of bounded deviations for homeomorphisms of closed surfaces of genus $\ge 2$. This first part studies bounded deviations with respect to closed geodesics. As a byproduct of our proofs, we also get a criterion of existence of periodic orbits in terms of big deviation with respect to some closed geodesic. The combination with the second part [arXiv:2511.14226] generalises to the higher genus case most of the bounded deviations results already known for the torus.

math.DS↗

arXiv2026

Bounded deviations in higher genus II: minimal laminations

This article follows and completes [arXiv:2511.14222], where we study the problem of bounded deviations for homeomorphisms of closed surfaces of genus $\ge 2$. This second part deals with bounded deviations relative to geodesic minimal laminations that are not reduced to a closed geodesic. The combination of both articles generalises to the higher genus case most of the bounded deviations results already known for the torus.

math.DS↗

arXiv2021

On proper extensions of the conformal group of sphere diffeomorphisms

In this paper, we prove that any group of diffeomorphisms acting on the 2-sphere and properly extending the conformal group of Möbius transformations must be at least 4-transitive or, more precisely, arc 4-transitive. In addition, we show that any such group must always contain an element of positive topological entropy. We also provide an elementary characterization, in terms of transitivity, of the Möbius transformations within the full group of sphere diffeomorphisms.

math.DS↗