3 papers
math.FA2018
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…
math.FA2017
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…
math.DS2015
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…