José Ignacio Extremiana Aldana

A closed model category for (-1)-connected spaces

For each integer n > 0, we give a distinct closed model category structure to the category of pointed spaces Top? such that the corresponding localized category Ho(Top? ) is equivalent to the standard homotopy category of (n− 1)-connected CW-complexes. The structure of closed model category given by Quillen to Top? is based on maps which induce isomorphisms on all homotopy group functors πq and for any choice of base point. For each n > 0, the closed model category structure given here takes as weak equivalences those maps that for the given base point induce isomorphisms on πq for q ≥ n .

Self-overlays and symmetries of Julia sets of expanding maps

When a semi-flow is induced by a d-fold branched covering

CW

f:M \rightarrow M

An approach to dynamical systems using exterior spaces

f:M→M defined on a Riemannian manifold M, the associated Julia set J(f) is a compact invariant subset of M and, therefore, there exists an induced restriction

The shape of the Julia set of an expanding rational map

f | _ {J (f)} :J (f) \rightarrow J (f)

Modelos de Quillen, espacios y flujos exteriores y algunas aplicaciones

f|J(f):J(f)→J(f). In order to construct an inverse system of regular sub-complexes whose inverse limit is J(f) we use computational techniques to iterate subdivision processes for a regular CW-structure given in M. The invariants of this inverse system can be used to study some topology and shape properties of J(f) . In particular, for the case of an expanding rational map we have constructed a resolution using global multipliers. The advantage of this resolution is that we can develop many algorithms that give an explicit description of the complexes of this resolution and implemented versions of this procedure can be used to give nice visualizations of the Julia set or to compute its shape invariants. If J(f) does not contain critical points of f, the restriction