This article presents results on expansive graphs that Víctor Neumann-Lara obtained in the late 1970’s and reported mostly without proofs in [8] and [9]. The untimely death of Víctor left us to complete this project, which had started in [7]. We had at hand [8, 9] and the manuscript [10] that, using his old notebooks, Víctor wrote with one of us in 1995. The original material has been thoroughl...

We prove that for C generic diffeomorphisms, every expansive homoclinic class is hyperbolic.

We call a dynamical system on a measurable metric space measureexpansive if the probability of two orbits remain close each other for all time is negligible (i.e. zero). We extend results of expansive systems on compact metric spaces to the measure-expansive context. For instance, the measureexpansive homeomorphisms are characterized as those homeomorphisms f for which the diagonal is almost in...

CSCL is based on the idea that computer applications can scaffold and implement advanced socio-cognitive processes for knowledge sharing and knowledge building. But do we really understand these processes that are supposed to be implemented? This paper will focus on the "epistemological infrastructure" of CSCL. We will analyze three models of innovative knowledge communities in order to better ...

This paper deals with the crises of long-term unemployment using subject theory, biographical research and critical theory as framework. Based on narrative-biographical interviews unemployed people, I identify factors conditions that turn into a crisis, arguing expansive learning processes competence utopian thinking are essential for creating visions one’s occupational future well (social) uto...

Motion planning for systems with constraints on controls or the need for relatively straight paths for real-time actions presents challenges for modern planners. This paper presents an approach which addresses these types of systems by building on existing motion planning approaches. Guided Expansive Spaces Trees are introduced to search for a low cost and relatively straight path in a space wi...

We introduce the notions of weakly and strongly positively expansive (wPE and sPE, respectively) discrete dynamical systems. Both are topological generalizations of the well-known metric notion of positive expansiveness (PE). We prove that the three notions are identical on compact metrizable spaces, but not on noncompact spaces. We investigate properties of PE, wPE, and sPE dynamical systems a...