Abstract

In this note, we present an example of a fibered dynamical system, also referred to as a deterministic random walk, generated by a piecewise linear expanding map on the first coordinate and a sign function on the second. We focus on the set of points whose orbits under this system remain non-negative in the second coordinate. Using the reflection principle from probability theory, we establish a connection between the topological pressure and a counting problem over constrained random walks. Furthermore, we show that the Hausdorff dimension of this set is invariant across horizontal sections and compute its Hausdorff measure. © 2025, MUK Publications and Distribution. All rights reserved.