2021-01-192021-01-192020-12-14JUCÁ, J. S. Conjuntos limite e transitividade de campos vetoriais suaves por partes em variedades Riemannianas bi-dimensionais. 2020. 86 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2020.http://repositorio.bc.ufg.br/tede/handle/tede/11039In this work we study piecewise-smooth vector fields defined on a two-di\-men\-sio\-nal differential manifold M, according to the Filippov convention. In the first part, M is considered as being any Riemannian manifold and we present a classification of the possible limit sets for a maximal trajectory whose its positive branch is contained on a compact subset $K\subset M$ (Theorem 3.1). We consider the occurrence of sliding motion and we verify the presence of limit sets with non-empty interior that can present a non-deterministic chaotic behavior. Moreover, we provide some examples and classes of systems satisfying the hypotheses of the main results. In the second part, we study the topological transitivity of piecewise-smooth vector fields defined on the two-dimensional sphere $S^2$. We guarantee the existence of an one-parameter family of topologically transitive piecewise-smooth vector fields on $S^2$ (Theorem 4.1), which does not happen for continuous vector fields on $S^2$. We prove that the occurrence of transitivity on $S^2$ implies the existence of escaping and sliding regions. We also prove they connect to each other through infinitely many Filippov trajectories. Moreover, we prove that there exist no robustly transitive piecewise-smooth vector fields on $S^2$.Attribution-NonCommercial-NoDerivatives 4.0 InternationalSistemas de FilippovCampos vetoriais suaves por partesConjuntos limiteTeorema de Poincaré-BendixsonMinimalidadeCaosTransitividade topológicaFilippov systemsPiecewise-smooth vector fieldsLimit setsPoincaré-Bendixson theoremMinimalityChaosTopological transitivityCIENCIAS EXATAS E DA TERRA::MATEMATICATese