Stratifications and Mappings††AMS (MOS) 1970 SUBJECT CLASSIFICATION: 58C25.‡‡This Chapter is based on lectures I gave at the Dynamical Systems conference. I wrote up these lectures partly during a stay at IMPA. I have developed these ideas over a period of years at Princeton, IHES, Harvard, and while supported by a Sloan fellowship and NSF grant GP-9566.I would like to thank all these institutions for their aid.
1973; Elsevier BV; Linguagem: Inglês
10.1016/b978-0-12-550350-1.50021-7
Autores Tópico(s)Geology and Paleoclimatology Research
ResumoThis chapter discusses stratifications and mappings. One of the fundamental objectives of the theory of singularities of mappings is to study the local structure of a smooth mapping. The local structure of a smooth mapping may be extremely complicated, for example, any closed subset of Euclidean space is the 0-set of some smooth real-valued function. The chapter also discusses the Whitney conditions, systems of tubular neighborhoods, locally integrable vector fields, polynomial mappings, and topological stability. To state Lojasiewicz's result, it discusses the notion of a semianalytic subset of a real analytic manifold. The chapter discusses the notion of an infinitesimally stable mapping, which is related to the notion of a smoothly stable mapping, considering the nonproper case where it turns out that infinitesimal stability is the more useful notion.
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