Geodesic
Topological conjugacy of cascades generated by gradient flows on the two-dimensional sphere
Annales Polonici Mathematici, Tome 73 (2000) no. 1, pp. 37-57

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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 obtained via the Euler method.
DOI : 10.4064/ap-73-1-37-57
Keywords: topological conjugacy, gradient dynamical system, Euler method

Andrzej Bielecki 1

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Andrzej Bielecki. Topological conjugacy of cascades generated by gradient flows on the two-dimensional sphere. Annales Polonici Mathematici, Tome 73 (2000) no. 1, pp. 37-57. doi: 10.4064/ap-73-1-37-57

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