arXiv subjects
Publications and source records attributed to Danilo Antonio Caprio.
In this work, we study properties of the coordinate functions $x_θ$ and $y_θ$ of the dragon curve associated with the angle $\fracπ{3} < θ< \frac{5π}{3}$, and we prove that the box-counting dimension of its graph is equal to $1 - \frac{\log \cosα}{\log 2}$, where $α= \frac{π- θ}{2}$.
In this work we consider a class of endomorphisms of $\mathbb{R}^2$ defined by $f(x,y)=(xy+c,x)$, where $c\in\mathbb{R}$ is a real number and we prove that when $-1<c<0$, the forward filled Julia set of $f$ is the union of stable manifolds of fixed and $3-$periodic points of $f$. We also prove that the backward filled Julia set of $f$ is the union of unstable manifolds of the saddle fixed and $3-$periodic points of $f$.
In this paper, we define some Markov Chains associated to Vershik maps on Bratteli diagrams. We study probabilistic and spectral properties of their transition operators and we prove that the spectra of these operators are connected to Julia sets in higher dimensions. We also study topological properties of these spectra.
In this work we define a stochastic adding machine associated to the Fibonacci base and to a probabilities sequence $\overline{p}=(p_i)_{i\geq 1}$. We obtain a Markov chain whose states are the set of nonnegative integers. We study probabilistic properties of this chain, such as transience and recurrence. We also prove that the spectrum associated to this Markov chain is connected to the fibered Julia sets for a class of endomorphisms in $\mathbb{C}^2$.