6 papers · 1 filter
Topology and dynamics of a flow that has a non-saddle set or a -set
Héctor Barge, J. J. Sánchez-Gabites, J. M. R. Sanjurjo
The aim of this paper is to study dynamical and topological properties of a flow in the region of influence of an isolated non-saddle set or a -set in a manifold. These are cert…
Shape index, Brouwer degree and Poincaré-Hopf theorem
Héctor Barge, José M. R. Sanjurjo
In this paper we study the relationship of the Brouwer degree of a vector field with the dynamics of the induced flow. Analogous relations are studied for the index of a vector fie…
Dissonant points and the region of influence of non-saddle sets
Héctor Barge, José M. R. Sanjurjo
The aim of this paper is to study dynamical and topological properties of a flow in the region of influence of an isolated non-saddle set. We see, in particular, that some topologi…
Fixed points, bounded orbits and attractors of planar flows
Héctor Barge, José M. R. Sanjurjo
In this paper we provide a dynamical characterization of isolated invariant continua which are global attractors for planar dissipative flows. As a consequence, a sufficient condit…
Dissipative flows, global attractors and shape theory
Héctor Barge, José M. R. Sanjurjo
In this paper we study continuous parametrized families of dissipative flows, which are those flows having a global attractor. The main motivation for this study comes from the obs…
Bifurcations, robustness and shape theory of attractors of discrete dynamical systems
Héctor Barge, Antonio Giraldo, José M. R. Sanjurjo
We study in this paper global properties, mainly of topological nature, of attractors of discrete dynamical systems. We consider the Andronov-Hopf bifurcation for homeomorphisms of…