It is known that any ε-expansive dynamical system with compact and totally disconnected domain can be embedded into a certain symbolic dynamical system. Actually, there exists a dynamical system with a compact and totally disconnected domain that cannot be topologically embedded into any symbolic dynamical system. Exactly speaking, ε-expansiveness plays an important role in the embedding problem. In this paper, the embedding theorem of dynamical systems which are not ε-expansive is discussed, and a relation between this result and the topological entropy is given.
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - 30 Nov 2005|
- Embedding theorem
- Lebesgue number
- Symbolic dynamical system
- ε-expansive dynamical system