The notes are based on lectures given in St. Flour in 1995, and cover, in greater detail, most
of the course given there. The word" fractal" was coined by Mandelbrot [Man] in the 1970s …

SuperFractals, first published in 2006, is the successor to Fractals Everywhere, in which the
power and beauty of Iterated Function Systems were introduced and applied to producing …

Assume that there is some analytic structure, a differential equation or a stochastic process
for example, on a metric space. To describe asymptotic behaviors of analytic objects, the …

Our main goal in this long survey article is to provide an overview of the theory of complex
fractal dimensions and of the associated geometric or fractal zeta functions, first in the case …

In this paper, we define the Green functions for a resistance form by using effective
resistance and harmonic functions. Then the Green functions and harmonic functions are …

The framework of post critically finite (pcf) self-similar fractals was introduced to capture the
idea of a finitely ramified fractal, that is, a connected fractal set where any component can be …

Transition density estimates for Brownian motion on scale irregular Sierphski gmkets Page 1
Ann. Inst. Henri Poincark, Vol. 33, no 5, 1997, p. 531-557 Transition density estimates for …

The theory of fractal strings and their complex dimensions investigates the geometric,
spectral and physical properties of fractals and precisely describes the oscillations in the …

Einstein proved that the mean square displacement of Brownian motion is proportional to
time. He also proved that the diffusion constant depends on the mass and on the …

We describe new families of random fractals, referred to as" V-variable", which are
intermediate between the notions of deterministic and of standard random fractals. The …