For a continuous map on the unit interval or circle, we define bifurcation set to be collection of those holes whose surviving is sensitive arbitrarily small changes (some of) their endpoints. By assuming global perspective and focusing geometric topological properties this rather than sets individual holes, obtain novel invariant for one-dimensional dynamics. We provide detailed description in...

A weighting of vertices of a graph is admissible if there exists an edge weighting such that the weight of each vertex equals the sum of weights of its incident edges. Given an admissible vertex weighting of a graph, an invariant set is an edge set such that the sum of the weights of its edges is the same for every edge weighting, and a nonempty invariant set is minimal if none of its nonempty ...

This paper offers a method for the computation of invariant approximations of the maximal invariant set for constrained linear discrete time systems subject to bounded, additive, disturbances. The main advantage of the method is that it generates invariant sets at any step of the underlying set iteration. Conditions under which the sequence of generated invariant sets is monotonically non–decre...