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

Volume 73 / 2000

Andrzej Bielecki Annales Polonici Mathematici 73 (2000), 37-57 DOI: 10.4064/ap-73-1-37-57


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.


  • Andrzej Bielecki

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