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

Andrzej Bielecki

Annales Polonici Mathematici (2000)

  • Volume: 73, Issue: 1, page 37-57
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Bielecki, Andrzej. "Topological conjugacy of cascades generated by gradient flows on the two-dimensional sphere." Annales Polonici Mathematici 73.1 (2000): 37-57. <http://eudml.org/doc/262842>.

@article{Bielecki2000,
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.},
author = {Bielecki, Andrzej},
journal = {Annales Polonici Mathematici},
keywords = {topological conjugacy; gradient dynamical system; Euler method; Morse-Smale system; Euler discretization},
language = {eng},
number = {1},
pages = {37-57},
title = {Topological conjugacy of cascades generated by gradient flows on the two-dimensional sphere},
url = {http://eudml.org/doc/262842},
volume = {73},
year = {2000},
}

TY - JOUR
AU - Bielecki, Andrzej
TI - Topological conjugacy of cascades generated by gradient flows on the two-dimensional sphere
JO - Annales Polonici Mathematici
PY - 2000
VL - 73
IS - 1
SP - 37
EP - 57
AB - 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.
LA - eng
KW - topological conjugacy; gradient dynamical system; Euler method; Morse-Smale system; Euler discretization
UR - http://eudml.org/doc/262842
ER -

References

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