The Dynamic Property of Lauwerier Mapping

Abstract

This paper uses the properties of the quadratic mapping. When an appropriate parameter a is chosen, the quadratic mapping fa has an attracting periodic orbit, and the attracting basin of the attracting periodic orbits is dense in a closed interval. An upper semi-continuous decomposition, G of the Lauwerier mapping is defined. There exists a decomposition space, G with respect to G. The properties of Lauwerier mapping is studied by the shift map on the inverse limit space of the quadratic mapping. The quadratic mapping is took nearly Markov partition. It is proved that Lauwerier mapping is topologically semi-conjugate to the shift mapping on the inverse limit space.