ERGODICITY AND ROBUST TRANSITIVITY ON THE REAL LINE / TRANSITIVIDADE ROBUSTA E ERGODICIDADE DE APLICAÇÕES NA RETA
AUTOR(ES)
MIGUEL ADRIANO KOILLER SCHNOOR
DATA DE PUBLICAÇÃO
2007
RESUMO
In the middle of the 19th century, G. Boole proved that the transformation x ->x ¿ 1/x, defined on R ¿ {0}, is a Lebesgue measure preserving transformation (Ble). Over one hundred years later, R. Adler and B.Weiss proved that this map, called Boole`s map, is, in fact, ergodic with respect to the Lebesgue measure (Adl). In this work, we present the notion of alternating systems, recently introduced by S. Mu`noz (Mun), which is a large class of functions on the real line that generalizes the Boole`s map and allows us to make a wide analysis on certain properties such as robust transitivity and ergodicity. In order to show that, under certain conditions, alternating systems are ergodic with respect to the Lebesgue measure, we show, using the Folklore Theorem, that the induced transformation of an alternating system is ergodic.
ASSUNTO(S)
sistemas alternantes alternating systems ergodicidade dinamica simbolica robust transitivity boole`s map transitividade robusta ergodicity symbolic dynamics transformacao de boole
