Narrow Results

This paper investigates the Weierstrass type function in local fields whose graph is a chaotic repelling set of a discrete dynamical system, and proves that their exists a linear connection between the orders of its p-adic calculus and the dimensions of the corresponding graphs.

The Weierstrass nowhere differentiable function has been studied often as example of functions whose graphs are fractals in ${ℝ}^2$. This paper investigates the Weierstrass-type function in the $p$-adic local field $K_p$ whose graph is a repelling set of a discrete dynamical system, and proves that there exists a linear connection between the orders of the $p$-adic calculus and the dimensions of the corresponding graphs.