THE C1 BRUNOVSKY HYPOTHESIS

[摘要] We prove that for the generic C1 arc of circle diffeomorphisms, t --> f(t), the rotation number t --> rho(f(t)) is a piecewise monotone function of t. A proof of this was attempted by Brunovsky in 1970. We also show that our methods cannot hope to answer the corresponding question for C(r) arcs of circle diffeomorphisms when r is greater-than-or-equal-to 2. (C) 1994 Academic Press, Inc.

[发布日期] 1994-10-15