Bernat Espigule

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20192026

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math.DS2026

Finite capture and the closure of roots of restricted polynomials

Bernat Espigule, David Juher

We study how a countable algebraic root set passes to a fractal connectedness locus. Let $D_{n} = {- n + 1, - n + 2, \dots, n - 1}$ , and let $R_{n}$ be the set of roots of monic polynomials whos…

math.DS2024

Collinear Fractals and Bandt's Conjecture

Bernat Espigule, David Juher, Joan Saldaña

For a complex parameter $c$ outside the unit disk and an integer $n \geq 2$ , we examine the $n$ -ary collinear fractal $E (c, n)$ , defined as the attractor of the iterated function syste…

math.DS2019

Families of connected self-similar sets generated by complex trees

Bernat Espigule

The theory of complex trees is introduced as a new approach to study a broad class of self-similar sets. Systems of equations encoded by complex trees tip-to-tip equivalence relati…