  The notion of topological equivalence plays an essential role in the study of
dynamical systems of flows. However, it is inherently difficult to generalize
this concept to systems without well-posedness in the sense of Hadamard. In
this study, we formulate a notion of "topological equivalence" between such
systems based on the axiomatic theory of topological dynamics proposed by
Yorke, and discuss its relation with the usual definition. During this process,
we generalize Yorke's theory to the action of topological groups.
