Matches in SemOpenAlex for { <https://semopenalex.org/work/W12720535> ?p ?o ?g. }
- W12720535 abstract "/ = ± ± '•• ± + const using suitable local coordinates. Every degenerate critical point bifurcates into some nondegenerate points after an arbitrarily small deformation (morsification). So generically, functions have no degenerate critical points. Degenerate critical points appear naturally when the function depends upon parameters. For example, the function f(x) = x — tx has a degenerate critical point for the value t = 0 of the parameter. Every family of functions close enough to this one-parameter family has a similar degenerate critical point for some small value of the parameter, When the parameters are few, only the simplest degeneracies appear generically, and one can explicitly list them, giving normal forms for functions and families. When the number of parameters increases, more complicated degeneracies appear, and their classification seems hopeless. In recent years it has been found, however, that at least the initial part of the hierarchy of singularities is remarkably simple, as is described below, Families of functions appear in all branches of analysis and mathematical physics. In this report three applications will be discussed: Lagrange singularities (or caustics), Legendre singularities (or wavefronts), and oscillating integrals (or stationary phase method)." @default.
- W12720535 created "2016-06-24" @default.
- W12720535 creator A5006200823 @default.
- W12720535 date "1975-01-01" @default.
- W12720535 modified "2023-09-27" @default.
- W12720535 title "Critical Points of Smooth Functions" @default.
- W12720535 cites W1563922012 @default.
- W12720535 cites W1603206290 @default.
- W12720535 cites W1605337527 @default.
- W12720535 cites W1963837917 @default.
- W12720535 cites W1964103416 @default.
- W12720535 cites W1970466164 @default.
- W12720535 cites W1998678324 @default.
- W12720535 cites W2004492171 @default.
- W12720535 cites W2005501195 @default.
- W12720535 cites W2006646657 @default.
- W12720535 cites W2009157351 @default.
- W12720535 cites W2011090652 @default.
- W12720535 cites W2016716371 @default.
- W12720535 cites W2029770333 @default.
- W12720535 cites W2033328505 @default.
- W12720535 cites W2035538452 @default.
- W12720535 cites W2051424471 @default.
- W12720535 cites W2070920936 @default.
- W12720535 cites W2077827904 @default.
- W12720535 cites W2078377537 @default.
- W12720535 cites W2082509446 @default.
- W12720535 cites W2085821474 @default.
- W12720535 cites W2086533250 @default.
- W12720535 cites W2102252392 @default.
- W12720535 cites W2103376167 @default.
- W12720535 cites W2136405887 @default.
- W12720535 cites W2141548614 @default.
- W12720535 cites W21573550 @default.
- W12720535 cites W2159626963 @default.
- W12720535 cites W219338751 @default.
- W12720535 cites W2312219160 @default.
- W12720535 cites W2314742144 @default.
- W12720535 cites W2316271461 @default.
- W12720535 cites W2319200503 @default.
- W12720535 cites W2338159400 @default.
- W12720535 cites W2366768275 @default.
- W12720535 cites W2617530992 @default.
- W12720535 cites W2911861088 @default.
- W12720535 cites W3018572680 @default.
- W12720535 cites W773130965 @default.
- W12720535 hasPublicationYear "1975" @default.
- W12720535 type Work @default.
- W12720535 sameAs 12720535 @default.
- W12720535 citedByCount "48" @default.
- W12720535 countsByYear W127205352012 @default.
- W12720535 countsByYear W127205352013 @default.
- W12720535 countsByYear W127205352014 @default.
- W12720535 countsByYear W127205352015 @default.
- W12720535 countsByYear W127205352016 @default.
- W12720535 countsByYear W127205352017 @default.
- W12720535 countsByYear W127205352018 @default.
- W12720535 countsByYear W127205352019 @default.
- W12720535 countsByYear W127205352020 @default.
- W12720535 countsByYear W127205352021 @default.
- W12720535 crossrefType "journal-article" @default.
- W12720535 hasAuthorship W12720535A5006200823 @default.
- W12720535 hasConcept C111458787 @default.
- W12720535 hasConcept C121332964 @default.
- W12720535 hasConcept C12843 @default.
- W12720535 hasConcept C134306372 @default.
- W12720535 hasConcept C14036430 @default.
- W12720535 hasConcept C153262748 @default.
- W12720535 hasConcept C196298200 @default.
- W12720535 hasConcept C202444582 @default.
- W12720535 hasConcept C2524010 @default.
- W12720535 hasConcept C2777727622 @default.
- W12720535 hasConcept C28719098 @default.
- W12720535 hasConcept C33923547 @default.
- W12720535 hasConcept C37914503 @default.
- W12720535 hasConcept C60644358 @default.
- W12720535 hasConcept C62520636 @default.
- W12720535 hasConcept C72319582 @default.
- W12720535 hasConcept C78458016 @default.
- W12720535 hasConcept C86803240 @default.
- W12720535 hasConceptScore W12720535C111458787 @default.
- W12720535 hasConceptScore W12720535C121332964 @default.
- W12720535 hasConceptScore W12720535C12843 @default.
- W12720535 hasConceptScore W12720535C134306372 @default.
- W12720535 hasConceptScore W12720535C14036430 @default.
- W12720535 hasConceptScore W12720535C153262748 @default.
- W12720535 hasConceptScore W12720535C196298200 @default.
- W12720535 hasConceptScore W12720535C202444582 @default.
- W12720535 hasConceptScore W12720535C2524010 @default.
- W12720535 hasConceptScore W12720535C2777727622 @default.
- W12720535 hasConceptScore W12720535C28719098 @default.
- W12720535 hasConceptScore W12720535C33923547 @default.
- W12720535 hasConceptScore W12720535C37914503 @default.
- W12720535 hasConceptScore W12720535C60644358 @default.
- W12720535 hasConceptScore W12720535C62520636 @default.
- W12720535 hasConceptScore W12720535C72319582 @default.
- W12720535 hasConceptScore W12720535C78458016 @default.
- W12720535 hasConceptScore W12720535C86803240 @default.
- W12720535 hasLocation W127205351 @default.
- W12720535 hasOpenAccess W12720535 @default.