# Shrinking-Targets for Non-Autonomous Systems

## TL;DR

This paper establishes a Bowen-type formula for the Hausdorff dimension of shrinking-target sets in non-autonomous conformal iterated function systems across dimensions, including conditions for perturbed systems.

## Contribution

It introduces a Bowen-type formula for non-autonomous systems and analyzes the effects of non-linear perturbations on these systems' dimensions.

## Key findings

- Derived a formula for Hausdorff dimension in non-autonomous systems
- Identified conditions for perturbed systems to satisfy the main hypotheses
- Extended results to non-linear perturbations in one dimension

## Abstract

In the present work we establish a Bowen-type formula for the Hausdorff dimension of shrinking-target sets for non-autonomous conformal iterated function systems in arbitrary dimensions and satisfying certain conditions. In the case of dimension 1 we also investigate non-linear perturbations of linear systems and obtain sufficient conditions under which the perturbed systems satisfy the conditions in our hypotheses