D. Caprio

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math.DS2025

Backward Julia sets for a class of p-adic Hénon like maps

Jéfferson L. R. Bastos, Danilo Caprio, Oyran Raizzaro

In this work we study the backward filled Julia sets of a class of $p$ -adic polynomial maps $f : Q_{p}^{2} ⟶ Q_{p}^{2}$ defined by $f (x, y) = (x y + c, x)$ , where $c\…

math.DS2025

The coordinate functions of the Heighway dragon curve

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 $\frac{π}{3} < θ < \frac{5 π}{3}$ , and we prove that the box…

math.DS2025

Operators of stochastic adding machines and Julia sets

Danilo Caprio, Ali Messaoudi, Ioannis Tsokanos +1

A stochastic adding machine is a Markov chain on the set of non-negative integers $Z_{+}$ that models the process of adding one by successively updating the digits of a nu…

math.DS2020

Shadowing and Stability in p-adic dynamics

Jéfferson Bastos, Danilo Caprio, Ali Messaoudi

In this paper, we study dynamical properties as shadowing and structural stability for a class of dynamics on $Z_{p}$ and $Q_{p}$ , where $p \geq 2$ is a prime number.…