简介：Risler&Trotmanin1997provedthatthemultiplicityofananalyticfunctiongermisleft-rightlipschitzinvariant,whichprovidedapartialanswertoZariskiconjecture.Inthisnote,basedontherecentworkofComte,Milman&Trotman,wegeneralizetheworkofthemtoprovethatthemultiplicityofaC~∞-differentiablefunctiongermisalsoleft-rightlipschitzinvariant.

简介：ThispaperestablishesthefollowingpointwiseresultforsimultancousLagrangeimterpolatingapproxima-tion:then|fk（x）-Pnk（f,x）|=O（1）△nq-k（x）ωwherePn（f,x）istheLagrangeinterpolatingpotynomialofdeereeonthenodesXnUYn（seethedefinitionofthenext）.

简介：ForthefamousFeigenbaum’sequations,inthispaper,weestablisheditsconstructivetheoremofthepeak-unimodal,thenwefoundoutotherpathstoexplorethepeak-unimodalsolutions.Forexample,weproceedonthedirectiontotrythenon-symmetricalcontinuouspeak-unimodalsolutionsandC~1solutions.