Equivalence of ill-posed dynamical systems

The problem of topological classification is fundamental in the study dynamical systems. However, when we consider systems without well-posedness, it unclear how to generalize notion equivalence. For example, a system has trajectories distinguished only by parametrization, cannot apply usual definition equivalence based on phase space, which presupposes uniqueness trajectories. In this study, formulate “topological equivalence” using axiomatic theory dynamics proposed Yorke [7], where are considered be shift-invariant subsets space partial maps. particular, type problems can regarded as invariants under morphisms between and generalized. This article intended also serve brief introduction ordinary differential equations (or dynamics) formalism presented [6].