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

Annales Polonici Mathematici (2000)

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

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topBielecki, 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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