从动力系统研究看当今数学界

§6.3... Milnor’s definition of “attractors” which has been criticized above by us).

   The work of [KSS2] of asserting the existence of “nice open set” of Ω(p.148) would be likely not verified, for example we think the first sentence “… since f is nontrivial, it has infinitely many periodic orbit…” in deducing Lemma 6.1 of [KSS1] needs to be explained. In [K1](p.748, the last paragraph) the author talked the existence of “nice intervals”, but we think his assertion would be only verified for certain quadratic-polynomial mappings, whereas [K1] is under certain general settings(see also [K2], p.7). ...

§6.5 We think the “Axiom A mappings” may not exist, because such mappings are required that “all periodic points are hyperbolic” which cannot be verified in general(see p.302 of [S]), and thus all involved works would be in vain.

[K1]O.Kozlovski, Getting rid of the negative Schwarzian derivative condition, Ann.of Math.152(2000),743-762.

[K2]O.Kozlovski, Axiom A mappings are dense in the space of unimodal maps in the

 topology, ibid, 157(2003), 1-43.

[KSS1]O.Kozlovski, W,Shen and S.v.Strien, Rigidity for real oplynomials, ibid,165(2007), 749-841.

[KSS2]O.Kozlovski, W,Shen and S.v.Strien, Density of hyperbolicity in dimension one, ibid, 166(2007), 145-182.

[S]W.Shen, On the metric properties of multimodal interval maps and  density of Axiom A, Invent. Math. 156(2004), 301-403.

----------------------------------------------------------

以上摘自我对动力系统方面工作的批判（在整个分析学的批判中列在§6）。从中发现一些实质错误，并看出沈维孝早在2004年（29岁）就已经在顶级刊物发表一篇100多页的论文，但也仅在国内弄到陈省身奖，在国际数学界似乎没啥名气，跟他合作的斯拉夫人O.Kozlovski似乎也类似。原因很简单，每年在几个国际顶级数学刊物发表论文的几百人，不可能都在国际数学界享有很高地位。更看出，沈维孝似乎已经参评院士4次都落空（从2004年起），算今年第5次，这反映了国内数学宗派主义很严重。剑桥大学三一学院的Alan Baker就是31岁获得Fields奖的。