المستخلص: |
In 1965, Adler R.L., Koheim A.G. and Mcandrew M.H., presented a definition of topological entropy with respect to cover and presented a definition of topological entropy as a continuous maps with respect to cover and then of topological entropy of continuous map with respect to all covers in order to reach at the entropy of Dynamical Systems as well as many characteristics of entropy on the different levels mentioned above. The Dissertation examined some of the relations between the characteristics presenting proofs which are suitable as a base for dependable topics through out the Dissertation. In 1969 Kolyada S. and Snoha L., presented definitions of topological entropy of a sequence of continuous maps and the equivalence between the definitions of Adler and Kolyada with the proof of their equivalence. This Dissertation is concerned with bi-entropy of bi-dynamical systems and it reached at some propositions and proofs presented for the first time in section two from chapter three, and there is an open equation about finding the entropy of sub shift by block map in a form suitable to the definitions presented in the compact spaces.
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