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Displaying similar documents to “The structure of orbits in dynamical systems”

Local invertibility

P. Doyle, J. Hocking, R. Osborne (1964)

Fundamenta Mathematicae

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Topological conjugacy of cascades generated by gradient flows on the two-dimensional sphere

Andrzej Bielecki (2000)

Annales Polonici Mathematici

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This article presents a theorem about the topological conjugacy of a gradient dynamical system with a constant time step and the cascade generated by its Euler method. It is shown that on the two-dimensional sphere S² the gradient dynamical flow is, under some natural assumptions, correctly reproduced by the Euler method for a sufficiently small time step. This means that the time-map of the induced dynamical system is globally topologically conjugate to the discrete dynamical system...