![]() His main research topic is Ergodic Theory. Toshihiro Hamachi is an Emeritus Professor at Kyushu University, Japan. In the same paper, the authors proved that every shift space Xcontains an entropy minimal subshift Y, i.e., a subshift Y of X such that h(Y) h(X). One is the Dyck shift and the other is the Fibonacci- Dyck shift. In fact, if Xis subshift of nite type with positive topological entropy, then Xcontains a subshift which is not of nite type, and hence contains in nitely many subshifts of nite type. In this talk as a target space we deal with two prototype subshifts in a certain class of subshifts which are quite different from SFT. It says that embedding is governed by two conjugacy invariants, the number of periodic points for a short period and topological entropy. When the target is an SFT too, there is a beautiful theorem known by W.Krieger to give an embedding condition. We are concerned with embedding of SFT's as a source in order to understand randomness of the target. In particular if the homeomorphism is onto, it is said to be a conjugacy. A homeomorphism from a subshift into another subshift is called an embedding if it intertwines the shift mappings. The shift mapping itself is also called a subshift. The shift mapping is defined on the space and turns out a homeomorphism. Namely two such sequences of the subshift are close if on a long time interval including time 0 they coincide. A subshift is endowed with the natural compact metric topology. It is known from various points of view that SFT's are quite random. When the set of forbidden words is finite, the subshift is called a shift of finite type (SFT). Given a finite alphabet the space of bi-infinite sequences of letters chosen from the alphabet is called a subshift when there is a set of words of the alphabet called forbidden words which do not appear in the sequences. ![]()
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