2ND TOPOLOGICAL CONJUGATE TRANSFORMATION IN SYMBOLIC DYNAMICS

A topological conjugate transformation defined as the joint actions of both the Derrida-Gervois-Pomeau (DGP) product operation QC* in the symbolic space (or its corresponding parameter space) and the mapping f(/QC/) in the symbolic dynamics of the interval, which with respect t o the first topological conjugate transformation (the merely action of QC) is called the second topological conjugate transformation, is fo und. It reveals conspicuously clustering of the orbital points and pre serves the topological entropy of the dynamical systems. In analogy to the first topological conjugate transformation, there exist also infi nitely many second topological conjugate maps. The second topological conjugate transformation provides a topological foundation for Feigenb aum's [J. Stat. Phys. 19, 25 (1978); 21, 669 (1979)] universalities an d a basic topological method for discriminating the compound words in the sense of the DGP product in the symbolic space Sigma(2), of two letters. Therefore it opens up a way to seek the generalized product for the more complex dynamical systems.