arXiv subjects

Antonio Giraldo

Publications and source records attributed to Antonio Giraldo.

2 recordsLinked to original sources

arXiv2018

Bifurcations, robustness and shape theory of attractors of discrete dynamical systems

We study in this paper global properties, mainly of topological nature, of attractors of discrete dynamical systems. We consider the Andronov-Hopf bifurcation for homeomorphisms of the plane and establish some robustness properties for attractors of such homeomorphisms. We also give relations between attractors of flows and quasi-attractors of homeomorphisms in Rn. Finally, we give a result on the shape (in the sense of Borsuk) of invariant sets of IFSs on the plane, and make some remarks about the recent theory of Conley attractors for IFS.

math.DS↗

arXiv2011

The Hessenberg matrix and the Riemann mapping

We consider a Jordan arc Γin the complex plane \mathbb{C} and a regular measure μwhose support is Γ. We denote by D the upper Hessenberg matrix of the multiplication by z operator with respect to the orthonormal polynomial basis associated with μ. We show in this work that, if the Hessenberg matrix D is uniformly asymptotically Toeplitz, then the symbol of the limit operator is the restriction to the unit circle of the Riemann mapping function ϕ(z) which maps conformally the exterior of the unit disk onto the exterior of the support of the measure μ. We use this result to show how to approximate the Riemann mapping function for the support of μfrom the entries of the Hessenberg matrix D.

math.SP↗