Dynamical systems, Measures and Fractals via Domain Theory Export

@misc{citeulike:1075727, abstract = {We introduce domain theory in dynamical systems, iterated function systems (fractals) and measure theory. For a discrete dynamical system given by the action of a continuous map f:X- X on a metric space X, we study the extended dynamical systems (l/X,l/f), (UX, U f) and (LX, Lf) where 1/, U and L are respectively the Vietoris hyperspace, the upper hyperspace and the lower hyperspace functors. We show that if (X, f) is chaotic, then so is (UX, U f). When X is locally compact UX, is a continuous...}, author = {Edalat, Abbas}, citeulike-article-id = {1075727}, citeulike-linkout-0 = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.5107}, keywords = {attractor, cantor-space, compactness, computable, computational-physics, distribution, domain-theory, dynamical-system, embedding, fixed-point, fractality, hyperspace, ifs, maximal-elements, measure-theory, powerdomains, self-similarity, t3-space, toological-space, upper-space, valuation, vietoris-space}, posted-at = {2007-01-30 09:51:10}, priority = {2}, title = {Dynamical systems, Measures and Fractals via Domain Theory}, url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.5107} }

TY - GEN ID - citeulike:1075727 L3 - citeulike-article-id:1075727 N2 - We introduce domain theory in dynamical systems, iterated function systems (fractals) and measure theory. For a discrete dynamical system given by the action of a continuous map f:X- X on a metric space X, we study the extended dynamical systems (l/X,l/f), (UX, U f) and (LX, Lf) where 1/, U and L are respectively the Vietoris hyperspace, the upper hyperspace and the lower hyperspace functors. We show that if (X, f) is chaotic, then so is (UX, U f). When X is locally compact UX, is a continuous... TI - Dynamical systems, Measures and Fractals via Domain Theory KW - attractor KW - cantor-space KW - compactness KW - computable KW - computational-physics KW - distribution KW - domain-theory KW - dynamical-system KW - embedding KW - fixed-point KW - fractality KW - hyperspace KW - ifs KW - maximal-elements KW - measure-theory KW - powerdomains KW - self-similarity KW - t3-space KW - toological-space KW - upper-space KW - valuation KW - vietoris-space AU - Edalat, Abbas UR - http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.5107 ER -