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- W1968563417 abstract "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, such that, say for the vector fields are in the class of hyperbolic vector fields described above, and 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" @default.
- W1968563417 created "2016-06-24" @default.
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- W1968563417 date "1997-01-01" @default.
- W1968563417 modified "2023-09-26" @default.
- W1968563417 title "Stability of hyperbolic vector fields" @default.
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- W1968563417 doi "https://doi.org/10.1080/02681119708806234" @default.
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