dc.creator | Bamon, A | |
dc.creator | Kiwi, J | |
dc.creator | Rivera Letelier, J | |
dc.creator | Urzua, R | |
dc.date.accessioned | 2024-01-10T12:41:09Z | |
dc.date.accessioned | 2024-05-02T17:21:46Z | |
dc.date.available | 2024-01-10T12:41:09Z | |
dc.date.available | 2024-05-02T17:21:46Z | |
dc.date.created | 2024-01-10T12:41:09Z | |
dc.date.issued | 2006 | |
dc.identifier | 10.1016/j.anihpc.2005.03.002 | |
dc.identifier | 1873-1430 | |
dc.identifier | 0294-1449 | |
dc.identifier | https://doi.org/10.1016/j.anihpc.2005.03.002 | |
dc.identifier | https://repositorio.uc.cl/handle/11534/77387 | |
dc.identifier | WOS:000235444200004 | |
dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/9268033 | |
dc.description.abstract | We study the dynamics of skew product endomorphisms acting on the cylinder R/Z x R, of the form | |
dc.description.abstract | (theta, t) -> (l theta, gimel t + tau(theta)), | |
dc.description.abstract | where l >= 2 is an integer, gimel is an element of (0, 1) and tau : R/Z -> R is a continuous function. We are interested in topological properties of the global attractor Omega(gimel,tau) of this map. Given l and a Lipschitz function tau, we show that the attractor set Omega(gimel,tau) is homeomorphic to a closed topological annulus for all gimel sufficiently close to 1. Moreover, we prove that Omega(gimel,tau) is a Jordan curve for at most finitely many gimel is an element of (0, 1). | |
dc.description.abstract | These results rely on a detailed study of iterated "cohomological" equations of the form tau = L gimel(1)mu(1),mu(1) = L gimel(2)mu(2),..., here L gimel mu = mu circle...circle m(l) - gimel mu and m(l) :R/Z -+ R/Z denotes the multiplication by l map. We show the following finiteness result: each Lipschitz function tau can be written in a canonical way as, | |
dc.description.abstract | tau = L gimel(1) circle...circle L gimel(m)mu, | |
dc.description.abstract | where m >= 0, gimel(1),...gimel(m) is an element of(0, 1] and the Lipschitz function mu satisfies mu = L gimel p for every continuous function p and every gimel is an element of (0,1]. | |
dc.description.abstract | (c) 2005 Published by Elsevier SAS. | |
dc.language | en | |
dc.publisher | ELSEVIER SCIENCE BV | |
dc.rights | acceso restringido | |
dc.subject | attractors | |
dc.subject | endomorphisms | |
dc.title | On the topology of solenoidal attractors of the cylinder | |
dc.type | artículo | |