On the Attractor of the Product System

Abstract

We investigate the attractor of the product system and mainly prove that the likely limit set of the product system equals the product of one of each factor system for n compact systems with solenoid attractors. Specially, this holds for the product map of Feigenbaum maps. Furthermore, we deduce that the Hausdorff dimension of the likely limit set of the product map for Feigenbaum maps is the sum of one of each factor map.