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# Chain recurrent sets of typical mappings

Ponente:
Cuándo 27/03/2012 de 17:00 a 19:00 Salón de seminarios Graciela Salicrup Sergio Macías vCal iCal

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.