Convergence Analysis of Transcendental Fractals

Convergence Analysis of Transcendental Fractals

Service Oriented Architectures are an abstract concept which exposes capabilities in distributed, domain-spanning environments as services. These modern systems have three characteristics: They are heterogeneous, distributed and loose Coupling. With increasing popularity of Service Oriented Architecture (SOA), this is no longer possible since interacting systems are generally not located within...

Invariance And Inner Fractals In Polynomial And Transcendental Fractals

A lot of formal and informal recreational study took place in the fields of Meromorphic Maps, since Mandelbrot popularized the map z ← z + c. An immediate generalization of the Mandelbrot z ← z + c also known as the Multibrot family were also studied. In the current paper, general truncated polynomial maps of the form z ← ∑ p≥2 apx p + c are studied. Two fundamental properties of these polynomi...

Analysis on Products of Fractals

For a class of post–critically finite (p.c.f.) fractals, which includes the Sierpinski gasket (SG), there is a satisfactory theory of analysis due to Kigami, including energy, harmonic functions and Laplacians. In particular, the Laplacian coincides with the generator of a stochastic process constructed independently by probabilistic methods. The probabilistic method is also available for non–p...

Groups and analysis on fractals

We describe relation between analysis on fractals and the theory of self-similar groups. In particular, we focus on the construction of the Laplacian on limit sets of such groups in several concrete examples, and in the general p.c.f. case. We pose a number of open questions.

Fractals in DNA sequence analysis