Convex delay endomorphisms |
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| Authors: | A Rovella F Vilamajó |
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| Institution: | (1) Centro de Matemática, Universidad de la República, Ed. Acevedo 1139, 11200 Montevideo, Uruguay;(2) IMERL-Facultad de Ingeniería, Universidad de la República CC 30, 11200 Montevideo, Uruguay;(3) Departament de Matemática Aplicada 2, Escola Tecnica Superior d'Enginyers Industrials, Colom 11, 08222 Terrassa, Barcelona, Espanya |
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| Abstract: | In this paper delay equationsx
n+k
=f(x
n
,...,x
n+k–1) are considered, where the functionf is supposed to be convex, having a unique point of maximum. It is proved that if there are no stationary solutions then all solutions must diverge. Considering the one parameter familyf
 =+f and associating to it a family of two dimensional mapsF
it is shown that the set of points having bounded orbit underF
is homeomorphic to the product of a Cantor set and a circle, and is hyperbolic and stable. |
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| Keywords: | |
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