Resumen en formato PDF - Departamento de Matemática Aplicada

Resumen en formato PDF - Departamento de Matemática Aplicada

SEMINARIO DEL DEPARTAMENTO
DE MATEMÁTICA APLICADA
Y ESTADÍSTICA
3
“PROFESOR FÉLIX MONDÉJAR”
CONFERENCIA
TÍTULO:
“Set-valued chaos”
CONFERENCIANTE:
MAREK LAMPART
Mathematical Institute, Silesian University
Opava (Czech Republic)
FECHA : JUEVES, 26 de mayo de 2005
HORA: 16,00H.
LUGAR: Salón de Actos de la E.U.I.T.Civil / E.T.S.I.N.O.
RESUMEN:
Let (X, d) be a compact metric space with a metric d and f : X «X a continuous map.
Let us consider the space (K(X), dH), where K(X) = {K ⊂ X, K is compact} and dH is
Hausdorff metric induced by d.
The main aim of this lecture is to discuss topological transitivity, weak mixing and
mixing for (set-valued) map f : K(X) →K(X) induced by f.
Namely, it was proved by [A. Peris, Chaos, Solitons & Fractals - to appear] that the
following three conditions are equivalent: (1) f is weakly mixing, (2) f is weakly mixing,
(3) f is topological transitive, and also that f is mixing if and only if f is mixing. The
assertion that f is topological transitive implies f is topological transitive was proved by
[H. Rom´an-Flores, Chaos, Solitons & Fractals 17 (2003) 99-104].
Finally, we prove that if f is chaotic in the sense of Li and Yorke then f is also chaotic in
the sense of Li and Yorke.