arXiv subjects

Jorge Iglesias

Publications and source records attributed to Jorge Iglesias.

9 recordsLinked to original sources

arXiv2026

Non-locally connected spaces I: Coverings and branched coverings on metric spaces

Whether a rational function can have an indecomposable continuum as its Julia set is a fundamental open problem in complex dynamics. We settle this negatively for one of the most classical examples of an indecomposable continuum: we prove that the Knaster continuum cannot be the Julia set of any rational function. To obtain this result, we develop a theory of coverings and branched coverings on general (non-locally connected) metric spaces. We introduce a new Euler characteristic and extend the Riemann--Hurwitz formula to a wider class of spaces, including continua for which the classical shape-theoretic invariants are trivial.

math.DS↗

arXiv2020

C0-Stability for actions implies shadowing property

We will construct an action $Φ$, C0 and C1-stable and we will prove that every C0-stable action acting in a manifold of dimensions greater or equal to two, have the shadowing property.

math.DS↗

arXiv2019

Shadowing Property for the free group acting in the circle

For the free group $F_2$ acting in $S^{1}$, we will prove that if the minimal set for the action is not a Cantor set, then the action does not have the shadowing property. We will also construct an example, whose minimal set is a Cantor set, that it has the shadowing property.

math.DS↗

arXiv2016

Examples of minimal set for IFSs

We exhibit different examples of minimal sets for an IFS of homeomorphisms with rotation number equal to 0. It is proved that these examples are, from a topological point of view, the unique possible cases.

math.DS↗

arXiv2016

Dynamics of covering maps of the annulus I: semiconjugacies

It is often the case that a covering map of the open annulus is semiconjugate to a map of the circle of the same degree. We investigate this possibility and its consequences on the dynamics. In particular, we address the problem of the classification up to conjugacy. However, there are examples which are not semiconjugate to a map of the circle, and this opens new questions.

math.DS↗

arXiv2016

Dynamics of annulus coverings II: periodic points

Let $f$ be a covering map of the open annulus $A= S^1\times (0,1)$ of degree $d$ , $|d|>1$. Assume that $f$ preserves an essential (i.e not contained in a disk of $A$) compact subset $K$. We show that $f$ has at least the same number of periodic points in each period as the map $z^d$ in $S^1.$

math.DS↗

arXiv2015

Robust transitivity for endomorphisms admitting critical points

We address the problem of giving necessary and sufficient conditions in order to have robustly transitive endomorphisms admitting persistent critical sets. We exhibit different type of open examples of robustly transitive maps in any isotopic class of endomorphisms acting on the two dimensional torus admitting persistent critical points. We also provide some necessary condition for robust transitivity in this setting.

math.DS↗

arXiv2014

About $C^{1}$-minimality of the hyperbolic Cantor sets

In this work we prove that a $C^{1+α}$-hyperbolic Cantor set contained in $S^1$, close to an affine Cantor set, is not $C^{1}$-minimal.

math.DS↗

arXiv2012

Surface Attractors

Let $f$ be a continuous endomorphism of a surface $M$, and $A$ an attracting set such that the restriction $f|_A: A \to A$ is a $d:1$ covering map. We show that if $f$ is a local homeomorphism in the immediate basin $B^0_A$ of $A$, then $f$ is also a $d:1$ covering of $B^0_A$.

math.DS↗