It is known that every hyperbolic Iterated Function System containing affine mappings can be represented in barycentric form by which it becomes affine invariant. Some properties were surveyed and some new ones were established. Examples of fractal sets supplement the theory.

In MU] there has been introduced and developed the concept of innnite conformal iterated function systems. In this paper we consider 1-dimensional systems. We provide necessary and suucient conditions for such systems to be bi-Lipschitz equivalent. We extend to such systems the concept of scaling functions and we pay special attention to the real-analytic systems.

The contribution of this paper is a new version of the escape time algorithm adapted to synthesize fractal images, identified with attractors of iterated function systems (IFS). The proposed synthesis algorithm is based on the use of shift dynamics, associated with one or another IFS. The novelty of the algorithm is grounded on two factors. Firstly, the strategy for the separation of extended d...

The implausibility of the extreme rationality assumptions of Nash equilibrium has been attested by numerous experimental studies with human players. In particular, the fundamental social dilemmas such as the Traveler’s dilemma, the Prisoner’s dilemma, and the Public Goods game demonstrate high rates of deviation from the unique Nash equilibrium, dependent on the game parameters or the environme...

We continue to study parabolic iterated function systems (IFS) with overlaps on the real line and invariant measures associated with them. A shift-invariant Borel probability measure on the coding space projects into a measure on the limit set of the IFS. We consider families of IFS depending on parameter and satisfying a certain \transversality" condition. In SSU2] suucient conditions were fou...

A fractal, as originally described by Mandelbrot, is a set with an irregular and fragmented shape. Many fractals that have been extensively studied, such as self-similar sets, have the same degree of irregularity and fragmentation at all length scales. In contrast to this, an equi-homogeneous set is an irregular and fragmented shape that at each fixed scale is identical at every point. We show ...

Most important outcome of Iterated Function System is Collage Theorem. In this consequence, IFS is designed in D-metric space . Finally Collage theorem is established in D-metric space structure. Mathematics Subject Classification: 28A80, 54H25

In this paper we give non-trivial applications of the thermodynamic formalism to the theory of distribution functions of Gibbs measures (devil’s staircases) supported on limit sets of finitely generated conformal iterated function systems in R. For a large class of these Gibbs states we determine the Hausdorff dimension of the set of points at which the distribution function of these measures i...

Multiple iterated revision needs advanced belief revision techniques beyond the classical AGM theory that are able to integrate several (propositional) pieces of new information into epistemic states. A crucial feature of this kind of revision is that the multiple pieces of information should be dealt with separately, which has usually been understood as requiring some kind of independence amon...

We consider conditional random quantities (c.r.q.’s) in the setting of coherence. Given a numerical r.q. X and a non impossible event H, based on betting scheme we represent the c.r.q. X|H as the unconditional r.q. XH + μH, where μ is the prevision assessed for X|H. We develop some elements for an algebra of c.r.q.’s, by giving a condition under which two c.r.q.’s X|H and Y |K coincide. We show...