4 citations · 12 across the 10 of their papers we have counts for
10 papers
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…
Integration in Čech theories and a bound on entropy
Luis Hernández-Corbato, David Jesús Nieves-Rivera, Francisco Romero Ruiz del Portal +1
The evaluation of Alexander-Spanier cochains over formal simplices in a topological space leads to a notion of integration of Alexander-Spanier cohomology classes over Čech homolog…
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…
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{…
Solving the social choice problem under equality constraints
J. A. Crespo, J. J. Sánchez-Gabites
In a context where a decision has to be taken collectively by several agents, the social choice problem consists in deciding whether there exists a socially acceptable rule that ag…
On the set of wild points of attracting surfaces in
J. J. Sánchez-Gabites
Suppose that a closed surface is an attractor, not necessarily global, for a discrete dynamical system. Assuming that its set of wild points is total…
On the shape of attractors of discrete dynamical systems
J. J. Sánchez-Gabites
Let be a manifold or (more generally) a locally compact, metrizable ANR. If is an attractor for a flow in , with basin of attraction , it is well known t…
Arcs, balls and spheres that cannot be attractors in
J. J. Sánchez-Gabites
For any compact set we define a number that is either a nonnegative integer or . Intuitively, provides some information on how wild…
Embedding of global attractors and their dynamics
Eleonora Pinto de Moura, James C. Robinson, Jaime J. Sánchez-Gabites
Using shape theory and the concept of cellularity, we show that if is the global attractor associated with a dissipative partial differential equation in a real Hilbert space $…
Unstable attractors in manifolds
J. J. Sánchez-Gabites
Let be a locally compact metric space endowed with a continuous flow . Frequently an attractor for exists which is of interest…