⎯This paper proposes fractal patterns for power quality (PQ) detection using color relational analysis (CRA) based classifier. Iterated function system (IFS) uses the non-linear interpolation in the map and uses similarity maps to construct various fractal patterns of power quality disturbances, including harmonics, voltage sag, voltage swell, voltage sag involving harmonics, voltage swell invo...

In a previous paper 12], we have shown that locally, in the vicinity of hyperbolic equilibria of autonomous ordinary diierential equations, the time-h-map of the induced dynamical system is conjugate to the h-discretized system i.e. to the discrete dynamical system obtained via one-step discretization with stepsize h. The present paper is devoted to Morse-Smale dynamical systems deened on plana...

In a previous paper 12], we have shown that locally, in the vicinity of hyperbolic equilibria of autonomous ordinary diierential equations, the time-h-map of the induced dynamical system is conjugate to the h-discretized system i.e. to the discrete dynamical system obtained via one-step discretization with stepsize h. The present paper is devoted to Morse-Smale dynamical systems deened on plana...

We provide several constructions of self-affine probability measures on the unit square with uniform marginals. These constructions include and extend constructions of previous authors and are parameterized in a natural way. In addition, for each different construction we determine the dimension of the parameter space and thus the level of flexibility (for instance, for approximation purposes) ...

A simple, yet unifying method is provided for the construction of tilings by tiles obtained from the attractor of an iterated function system (IFS). Many examples appearing in the literature in ad hoc ways, as well as new examples, can be constructed by this method. These tilings can be used to extend a fractal transformation defined on the attractor of a contractive IFS to a fractal transforma...

We study the decidability of some properties of self-affine sets specified by a graph-directed iterated function system (GIFS) with rational coefficients. We focus on topological properties and we prove that having empty interior is undecidable in dimension two. These results are obtained by studying a particular class of self-affine sets associated with multitape automata. We first establish t...

Using techniques introduced by C. Güntürk, we prove that the attractors of a family of overlapping self-affine iterated function systems contain a neighbourhood of zero for all parameters in a certain range. This corresponds to giving conditions under which a single sequence may serve as a ‘simultaneous β-expansion’ of different numbers in different bases.

We introduce a geometric condition of Bloch type which guarantees that a subset of a bounded convex domain in several complex variables is degenerate with respect to every iterated function system. Furthermore we discuss the relations of such a Bloch type condition with the analogous hyperbolic Lipschitz condition.