Dual star products and symbolic dynamics of Lorenz maps with the same entropy

Dual star products * is an element of {(*) over bar,(*) under bar} of the k neading sequence pairs for two-parameter families of Lorenz maps on the int erval are presented in the topological space of two letters. The dual star products support the first topological conjugate invariant and lead to one of the statements of the generalized Milnor-Thurston conjecture to be valid . These results are more complicated than that of bimodal maps. The dual Fe igenbaum's metric universality and the form of unified dual star products f or continuous and piece-wise continuous maps exist. (C) 1999 Published by E lsevier Science B.V. All rights reserved.