Chain recurrent sets of typical mappings
Profesor Konrad Ungeheue de la Universidad de Wroclaw
Cuándo |
27/03/2012 de 17:00 a 19:00 |
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Dónde | Salón de seminarios Graciela Salicrup |
Nombre | Sergio Macías |
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Resumen: Let X be a compact, metric space. Denote by C(X,X) the space of all continuous self-maps of X with the topology of uniform convergence. Given f \in C(X,X) and \epsilon > 0, an \epsilon-chain in X from x to y is a finite sequence: x_0, x_1, x_2, ... ,x_n where x_0 = x and x_n = y, such that d(f (x_{i-1}), x_i ) < \epsilon for i=1, ... ,n. A point x is chain recurrent if there is an \epsilon-chain from x to x for any \epsilon > 0. By CR(f) we denote the set of all chain recurrent points of f. We going to investigate the properties of the class 0-CR of compact metric spaces X such that the set {f \in C(X,X); dim(CR(f)) = 0} is dense G_\delta in C(X,X). It is known that graphs, PL manifolds of dimension at least 2, finite-dimensional polyhedra and many others are in 0-CR. More examples of members of class 0-CR will be presented.