Results 51 to 60 of about 15,237 (204)
Real Projective Iterated Function Systems [PDF]
Journal of Geometric Analysis, 2011 This paper contains four main results associated with an attractor of a projective iterated function system (IFS). The first theorem characterizes when a projective IFS has an attractor which avoids a hyperplane. The second theorem establishes that a projective IFS has at most one attractor. In the third theorem the classical duality between points and
Barnsley, Michael F., Vince, Andrew
openaire +4 more sources
Sampling and interpolation of cumulative distribution functions of Cantor sets in [0, 1]
Demonstratio Mathematica, 2021 Cantor sets are constructed from iteratively removing sections of intervals. This process yields a cumulative distribution function (CDF), constructed from the invariant Borel probability measure associated with their iterated function systems.
Byars Allison +5 more
doaj +1 more source
Iterated function systems consisting of continuous functions satisfying Banach’s orbital condition
Annals of the West University of Timisoara: Mathematics and Computer Science, 2018 We introduce the concept of iterated function system consisting of continuous functions satisfying Banach’s orbital condition and prove that the fractal operator associated to such a system is weakly Picard. Some examples are provided.
Miculescu Radu +2 more
doaj +1 more source
Nonlinear Fractal Interpolation Functions Induced by General Integral Contractions
Fractal and FractionalThe development of fractal set theory has been strongly driven by the introduction of new classes of fractal sets, among which the attractors of iterated function systems (IFSs) play a central role.
Taoufik Moulahi, Najmeddine Attia
doaj +1 more source
Mathematical Modeling of Fractals via Proximal F-Iterated Function Systems
AxiomsWe propose a novel approach to fractals by leveraging the approximation of fixed points, emphasizing the deep connections between fractal theory and fixed-point theory.
Muhammad Zahid +4 more
doaj +1 more source
Fixed point theorems for nonlinear contractions with applications to iterated function systems
Applied General Topology, 2018 We introduce a new type of nonlinear contraction and present some fixed point results without using continuity or semi-continuity. Our result complement, extend and generalize a number of fixed point theorems including the the well-known Boyd and Wong ...
Rajendra Pant
doaj +1 more source
C^1 robustly minimal iterated function systems
, 2010 We construct iterated function systems on compact manifolds that are C^1 robustly minimal. On the m-dimensional torus and on two-dimensional compact manifolds, examples are provided of C^1 robustly minimal iterated function systems that are generated by ...
Homburg, A.J. +2 more
core +1 more source
Iterated function systems of logistic maps: Synchronization and intermittency [PDF]
, 2018 We discuss iterated function systems generated by finitely many logistic maps, with a focus on synchronization and intermittency. We provide sufficient conditions for synchronization, involving negative Lyapunov exponents and minimal dynamics.
Gharaei, M. +8 more
core +1 more source
Graph-Theoretic Characterization of Separation Conditions in Self-Affine Iterated Function Systems
Fractal and FractionalFor a self-affine iterated function system (IFS) {fj}j=1N on Rd defined by fj(x)=A−1(x+dj), where A is an expansive matrix and dj∈Rd, we reveal a novel characterization of the open set and weak separation conditions through the bounded degree of the ...
Ming-Qi Bai, Jun Luo, Yi Wu
doaj +1 more source
The similarity dimension of the random iterated function system [PDF]
Компьютерные исследования и моделирование, 2012 In this paper we consider the properties of the random iterated function systems (RIFS) obtained using a generalization of the Chaos game algorithm. Used for the RIFS simulation R is a free software environment for statistical computing and graphics. The
Pavel Valentinovich Moskalev +1 more
doaj +1 more source