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...

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...

Expansive soils are often encountered in many parts of the world, especially in arid and semi-arid fields. Such kind of soils, generally including active clay minerals in low water content, enlarge in volume by absorbing the water through the surface and cause a great harm to the light structures such as channel coating, roads and airports. The expansive soils were encountered on the path of Ap...

The firing rates of neurons in the central visual pathway vary with stimulus strength, but not necessarily in a linear manner. In the contrast domain, the neural response function for cells in the primary visual cortex is characterized by expansive and compressive nonlinearities at low and high contrasts, respectively. A compressive nonlinearity at high contrast is also found for early visual p...