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- Fine properties of Lp-cocycles which allow abundance of simple and trivial spectrumPublication . Bessa, Mário; Vilarinho, HelderIn this paper we prove that the class of accessible and saddle-conservative cocycles (a wide class which includes cocycles evolving in GL(d,R), SL(d,R) and Sp(d,R)) Lp-densely have a simple spectrum. We also prove that for an Lp-residual subset of accessible cocycles we have a one-point spectrum. Finally, we show that the linear differential system versions of previous results also hold and give some applications.
- Stretching generic pesin’s entropy formulaPublication . Bessa, Mário; Silva, César M.; Vilarinho, HelderWe prove that Pesin’s entropy formula holds generically within a broad subset of volume-preserving bi-Lipschitz homeomorphisms with respect to the Lipschitz–Whitney topology.