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Details van artikel 100 van 114 gevonden artikelen
| Titel: |
Stability of hyperbolic vector fields |
| Auteur: |
Plaza, Sergio Vera, Jaime |
| Verschenen in: |
Dynamical systems |
| Paginering: | Jaargang 12 (1997) nr. 1 pagina's 25-37 |
| Jaar: |
1997 |
| Inhoud: |
We give a geometrical proof of the global stability theorem for a large class of hyperbolic vector fields (i. e. those satisfying axiom A and the strong transversality condition). The class of hyperbolic vector fields we consider in this paper is constituted by those hyperbolic vector fields for which the attractor and repellor sets are trivial (i. e. singularities and/or periodic orbits) and their non-trivial basic sets are d-separated. We apply the geometrical proof in order to study elementary bifurcations of one-parameter families of vector fields[image omitted] , such that, say for[image omitted] the vector fields[image omitted] are in the class of hyperbolic vector fields described above, and [image omitted] has an elementary generic bifurcation, i. e. (i) a saddle-node or a Hopf singularity; (ii) a saddle-node or a flip periodic orbit; (iii) a quasi-transversal intersection orbit between an unstable and a stable manifold; all of which are generic bifurcations that unfold genetically at the parameter bifurcation value[image omitted] |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 100 van 114 gevonden artikelen
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