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- W996896491 abstract "Publisher Summary This chapter focuses on moduli of stability for gradients. Investigations of structural stability, especially in a context of genericity, have played an important role in the study of dynamical systems in the last decades. It was found that on (orientable) surfaces, generic vector fields are structurally stable. It turned out that generic one-parameter families of gradient vector fields are structurally stable. There are also strong indications that the same holds for two-parameter families. This led to the problem whether generic k-parameter families of gradients are structurally stable, or at most would only have a “finite number of moduli of stability.” The chapter explains that: (i) it is not a generic property of k -parameter families of gradient vector fields on an n -manifold to be structurally stable, at least not if k ≥ 8 and n ≥ 3; (ii) it is not a generic property of k -parameter families of gradient vector fields on an n -manifold to have only a finite number of moduli of stability, at least not if k ≥ 16 and n ≥ 4." @default.
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- W996896491 date "1985-01-01" @default.
- W996896491 modified "2023-09-27" @default.
- W996896491 title "Moduli of Stability for Gradients" @default.
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- W996896491 doi "https://doi.org/10.1016/s0304-0208(08)72117-0" @default.
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