https://hdl.handle.net/20.500.12008/46869 2026-05-13T12:10:26Z https://hdl.handle.net/20.500.12008/54929 Título: Robustly transitive maps with critical points and large dimensional central spaces Autor: Morelli, Juan Carlos Resumen: Given any triplet of positive integers n ≥ 2, m and k such that n = m + k, we exhibit a C1 robustly transitive endomorphism of Tn with persistent critical points in the isotopy class of F ×Id, where F is an expanding map of Tm and Id is the identity of Tk. Furthermore, if k is small, the map is not only in the isotopy class but in fact a perturbation of F × Id. 2026-01-01T00:00:00Z https://hdl.handle.net/20.500.12008/54928 Título: Generic homeomorphisms with shadowing of one-dimensional continua Autor: Artigue, Alfonso; Cousillas, Gonzalo Resumen: In this article we show that there are homeomorphisms of plane continua whose conjugacy class is residual and have the shadowing property. 2019-01-01T00:00:00Z https://hdl.handle.net/20.500.12008/54927 Título: A fixed point theorem for plane homeomorphisms with the topological shadowing property Autor: Cousillas, Gonzalo Resumen: In this paper we show that every homeomorphism of the plane with the topological shadowing property has a fixed point. Also, we show that a linear isomorphism of an Euclidean space has the topological shadowing property if and only if the origin is an attractor or a repeller. 2019-01-01T00:00:00Z https://hdl.handle.net/20.500.12008/54926 Título: Graded braided commutativity in Hochschild cohomology Autor: Cóppola, Javier; Solotar, Andrea Resumen: We prove the graded braided commutativity of the Hochschild cohomology of A with trivial coefficients, where A is a braided Hopf algebra in the category of Yetter- Drinfeld modules over the group algebra of an abelian group, under some finiteness conditions on a projective resolution of A as A-bimodule. This is a generalization of a result by Mastnak, Pevtsova, Schauenburg and Witherspoon to a context which includes Nichols algebras such as the Jordan and the super Jordan plane. We prove this result by constructing a coduoid-up-to-homotopy structure on the aforementioned projective resolution in the duoidal category of chain complexes of A-bimodules. We also prove that the Hochschild complex of a braided bialgebra A in an arbitrary braided monoidal category is a cocommutative comonoid up to homotopy with the deconcatenation product which induces the cup product in Hochschild cohomology. 2022-01-01T00:00:00Z