Nondifferentiable Dynamical Systems.
NAVAL POSTGRADUATE SCHOOL MONTEREY CALIF
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The study of dynamical systems originated as a topological analysis method in the field of stability theory concerning autonomous ordinary differential equations. The dynamical system is not restricted by definition to differential systems, and the results presented here were obtained without hypothesizing differentiability of the dynamical system. The most significant results were that the level surfaces of Lyapunov function for a compact asymptotically stable set in R sup n are orientable n-1-dimensional generalized closed manifolds, that every asymptotically stable periodic trajectory in R sup 3 is tamely imbedded in R sub 3, and that a periodic dynamical system on a compact 2-manifold is equivalent to an S sup 1 action. Author
- Theoretical Mathematics