7 citations · 39 across the 14 of their papers we have counts for
14 papers
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…
On the growth rate inequality for self-maps of the sphere
Héctor Barge, Luis Hernández-Corbato
Let and . Suppose that is a self--map of such that and $|\mathrm{deg}(f_{|P…
Knotted toroidal sets, attractors and incompressible surfaces
Héctor Barge, J. J. Sánchez-Gabites
In this paper we give a complete characterization of those knotted toroidal sets that can be realized as attractors for both discrete and continuous dynamical systems globally defi…
Higher dimensional topology and generalized Hopf bifurcations for discrete dynamical systems
Héctor Barge, José M. R. Sanjurjo
In this paper we study generalized Poincaré-Andronov-Hopf bifurcations of discrete dynamical systems. We prove a general result for attractors in n-dimensional manifolds satisfying…
Cech cohomology, homoclinic trajectories and robustness of non-saddle sets
Héctor Barge
In this paper we study flows having an isolated non-saddle set. We see that the complexity of the region of influence of an isolated non-sadd…
The geometric index and attractors of homeomorphisms of
H. Barge, J. J. Sánchez-Gabites
In this paper we focus on compacta which possess a neighbourhood basis that consists of nested solid tori . We call these sets toroidal. In \cite{he…
A Conley index study of the evolution of the Lorenz strange set
Héctor Barge, J. M. R. Sanjurjo
In this paper we study the Lorenz equations using the perspective of the Conley index theory. More specifically, we examine the evolution of the strange set that these equations po…
Knots and solenoids that cannot be attractors of self-homeomorphisms of
Héctor Barge, J. J. Sánchez-Gabites
As a first step to understand how complicated attractors for dynamical systems can be, one may consider the following realizability problem: given a continuum $K \subseteq \mathbb{…
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…
Regular blocks and Conley index of isolated invariant continua in surfaces
Héctor Barge
In this paper we study topological and dynamical features of isolated invariant continua of continuous flows defined on surfaces. We show that near an isolated invariant continuum…
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…