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On the classification of dynamical systems. (English) Zbl 0675.58022
The following program concerning the classification of the smooth vector fields from the space V on a manifold is proposed: (1) Choose an equivalence relation V, and define a vector field to be stable if it has a neighbourhood of equivalents in V. (2) Prove that the stables are dense in V. (3) Classify the stable classes. (4) Classify the unstable classes of codimension 1,2,..., etc.
This is then discussed and illustrated by means of four fundamental theorems. Four related examples are also chosen sensitively to clarify every single step of the above schedule.
Reviewer: J.Andres

MSC:
37C75 Stability theory for smooth dynamical systems
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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