A global two-dimensional version of Smale's cancellation theorem via spectral sequences

作者：Bertolim M A^*; Lima D V S; Mello M P; De Rezende K A; Da Silveira M R

来源：Ergodic Theory and Dynamical Systems, 2016, 36(06): 1795-1838.

DOI：10.1017/etds.2014.142

In this article, Conley's connection matrix theory and a spectral sequence analysis of a filtered Morse chain complex (C, Delta) are used to study global continuation results for flows on surfaces. The briefly described unfoldings of Lyapunov graphs have been proved to be a well-suited combinatorial tool to keep track of continuations. The novelty herein is a global dynamical cancellation theorem inferred from the differentials of the spectral sequence (E-r, d(r)). The local version of this theorem relates differentials dr of the r th page E-r to Smale's theorem on cancellation of critical points.

• 出版日期2016-9