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ArticleOriginal scientific text

Title

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

Authors 1

Affiliations

  1. Institute of Computer Science, Jagiellonian University, Nawojki 11, 30-072 Kraków, Poland

Abstract

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.

Keywords

ENG
topological conjugacy, gradient dynamical system, Euler method

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Annales Polonici Mathematici
2000/73/1
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Pages:
37-57
Main language of publication
English
Received
1998-02-18
Accepted
1999-12-08
Published
2000
Exact and natural sciences