A global two-dimensional version of Smale’s cancellation theorem via spectral sequences
| Autor: | Maria Alice Bertolim, M. R. Da Silveira, Dahisy V. S. Lima, Margarida P. Mello, K. A. de Rezende |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Ergodic Theory and Dynamical Systems. 36:1795-1838 |
| ISSN: | 1469-4417 0143-3857 |
| DOI: | 10.1017/etds.2014.142 |
| Popis: | In this article, Conley’s connection matrix theory and a spectral sequence analysis of a filtered Morse chain complex $(C,{\rm\Delta})$ 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 $d^{r}$ of the $r$th page $E^{r}$ to Smale’s theorem on cancellation of critical points. |
| Databáze: | OpenAIRE |
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