1 citations · 1 across the 4 of their papers we have counts for
6 papers
Fixed Points of anti-attracting maps and Eigenforms on Fractals
Roberto Peirone
An important problem in analysis on fractals is the existence of a self-similar energy on finitely ramified fractals. The self-similar energies are constructed in terms of eigenfor…
A P.C.F. Self-Similar Set with no Self-Similar Energy
Roberto Peirone
A general class of finitely ramified fractals is that of P.C.F. self-similar sets. An important open problem in analysis on fractals was whether there exists a self-similar energy…
Scaling Distances on Finitely Ramified Fractals
Roberto Peirone
In previous papers by A. Kameyama and by J. Kigami distances on fractals have been discussed having two different but similar properties. One property is that the maps defining the…
Attractors of Iterated Function Systems with uncountably many maps
Giorgio Mantica, Roberto Peirone
We study the topological properties of attractors of Iterated Function Systems (I.F.S.) on the real line, consisting of affine maps of homogeneous contraction ratio. These maps def…
Uniqueness of Eigenforms on Fractals-II
Roberto Peirone
I give an explicitly verifiable necessary and sufficient condition for the uniqueness of the eigenform on finitely ramified fractals, once an eigenform is known. This improves the…
Integrals of convex functions in the gradients on fractals
Roberto Peirone
In this paper, I describe the construction of certain functional integrals in the gradient on finitely ramified fractals, which have a sort of self-similarity property.