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Isolating blocks for Morse flows |
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| Authors: | Maria Alice Bertolim Ketty Abaroa de Rezende Oziride Manzoli Neto Gioia M. Vago |
| Affiliation: | 1. IMB—UMR 5584 du CNRS, Université de Bourgogne, Dijon, France 2. Imecc– Unicamp, Instituto de Matemática, Estatística e Computa??o Científica, Universidade Estadual de Campinas, Campinas, SP, Brazil 3. Instituto de Ciências Matemáticas e de Computa??o, Universidade de S?o Paulo, S?o Carlos, SP, Brazil |
| Abstract: | We present a constructive general procedure to build Morse flows on n-dimensional isolating blocks respecting given dynamical and homological boundary data recorded in abstract Lyapunov semi-graphs. Moreover, we prove a decomposition theorem for handles which, together with a special class of gluings, insures that this construction not only preserves the given ranks of the homology Conley indices, but it is also optimal in the sense that no other Morse flow can preserve this index with fewer singularities. |
| Keywords: | Conley index theory Morse flows Lyapunov graphs |
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