; ▁the ▁visible ▁is ▁the ▁stable . ▁Whit ney ▁had ▁shown ▁that ▁in ▁low ▁numbers ▁of ▁variables ▁the ▁stable ▁structure ▁of ▁critical ▁points ▁is ▁very ▁restricted , ▁in ▁local ▁terms . ▁Thom ▁built ▁on ▁this , ▁and ▁his ▁own ▁earlier ▁work , ▁to ▁create ▁a ▁cat ast rop he ▁theory ▁supposed ▁to ▁account ▁for ▁dis continu ous ▁change ▁in ▁nature . ▁ ▁Arnold ' s ▁view ▁While ▁Thom ▁was ▁an ▁em inent ▁math ematic ian , ▁the ▁subsequent ▁fashion able ▁nature ▁of ▁elementary ▁cat ast rop he ▁theory ▁as ▁propag ated ▁by ▁Christopher ▁Ze eman ▁caused ▁a ▁reaction , ▁in ▁particular ▁on ▁the ▁part ▁of ▁Vladimir ▁Arnold . ▁He ▁may ▁have ▁been ▁largely ▁responsible ▁for ▁applying ▁the ▁term ▁singular ity ▁theory ▁to ▁the ▁area ▁including ▁the ▁input ▁from ▁algebraic ▁geometry , ▁as ▁well ▁as ▁that ▁flow ing ▁from ▁the ▁work ▁of ▁Whit ney , ▁Thom ▁and ▁other ▁authors . ▁He ▁wrote ▁in ▁terms ▁making ▁clear ▁his ▁dist aste ▁for ▁the ▁too - public ised ▁emphas is ▁on ▁a ▁small ▁part ▁of ▁the ▁territory . ▁The ▁found ational ▁work ▁on ▁smooth ▁singular ities ▁is ▁form ulated ▁as ▁the ▁construction ▁of ▁equivalence ▁relations ▁on ▁singular ▁points , ▁and ▁germ s . ▁Techn ically ▁this ▁involves ▁group ▁actions ▁of ▁Lie ▁groups ▁on ▁spaces ▁of ▁j ets ; ▁in ▁less ▁abstract ▁terms ▁Taylor ▁series ▁are ▁exam ined ▁up ▁to ▁change ▁of ▁variable , ▁pin ning ▁down ▁singular ities ▁with ▁enough ▁derivatives . ▁App lications , ▁according ▁to ▁Arnold , ▁are ▁to ▁be ▁seen ▁in ▁sym ple ctic