https://hdl.handle.net/20.500.12008/46870 Sat, 06 Jun 2026 23:47:44 GMT 2026-06-06T23:47:44Z https://hdl.handle.net/20.500.12008/55055 Título: Structurally stable perturbations of polynomials in the Riemann sphere Autor: Iglesias, Jorge; Portela, Aldo; Rovella, Álvaro Resumen: The perturbations of complex polynomials of one variable are considered in a wider class than the holomorphic one. It is proved that under certain conditions on a polynomial p of the plane, the conjugacy class of a map f in a neighborhood of p depends only on the geometric structure of the critical set of f. This provides the first class of examples of structurally stable maps with critical points and nontrivial nonwandering set in dimension greater than one.; Nous considérons les perturbations des polynômes complexes en une variable dans une classe plus vaste que la classe holomorphe. Si f est une application appartenant à un voisinage d'un polynôme p du plan, nous prouvons, sous certaines conditions sur p, que la classe de conjugaison de f ne dépend que de la structure géométrique du lieu critique de f. Ceci fournit la première classe d'exemples, en dimension supérieure à une, d'applications structurellement stables ayant des points critiques et un ensemble nonerrant nontrivial. Tue, 01 Jan 2008 00:00:00 GMT https://hdl.handle.net/20.500.12008/55055 2008-01-01T00:00:00Z https://hdl.handle.net/20.500.12008/55052 Título: Golden tilings Autor: Pinto, A. A.; Almeida, J.P.; Portela, Aldo Resumen: We introduce the notion of golden tilings, and we prove a one-to-one correspondence between (i) smooth conjugacy classes of Anosov diffeomorphisms, with an invariant measure absolutely continuous with respect to the Lebesgue measure, (ii) affine classes of golden tilings and (iii) solenoid functions. The solenoid functions give a parametrization of the infinite dimensional space consisting of the mathematical objects described in the above equivalences. Sun, 01 Jan 2012 00:00:00 GMT https://hdl.handle.net/20.500.12008/55052 2012-01-01T00:00:00Z https://hdl.handle.net/20.500.12008/55042 Título: Attracting sets on surfaces Autor: Iglesias, Jorge; Portela, Aldo; Rovella, Álvaro; Xavier, Juliana Resumen: Let f be a continuous endomorphism of a surface M, and A an attracting set such that the restriction f|A : A → A is a d : 1 covering map. We show that if f is a local homeomorphism, then f is also a d : 1 covering of the immediate basin of A. Moreover, the techniques provide a characterization of invariant d : 1 continua on surfaces. These results are no longer true on manifolds of dimensions at least three. Thu, 01 Jan 2015 00:00:00 GMT https://hdl.handle.net/20.500.12008/55042 2015-01-01T00:00:00Z https://hdl.handle.net/20.500.12008/55006 Título: Periodic points of covering maps of the annulus Autor: Iglesias, Jorge; Portela, Aldo; Rovella, Álvaro; Xavier, Juliana Resumen: Let f be a covering map of the open annulus A = S1 × (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 zd in S1. Descripción: Publicado en arXiv y en Fundamenta Mathematicae, 235 (2016), pp. 257-276, con el titulo "Dynamics of annulus maps II: Periodic points for coverings". Fri, 01 Jan 2016 00:00:00 GMT https://hdl.handle.net/20.500.12008/55006 2016-01-01T00:00:00Z