Intent detection, a fundamental text classification task, aims to identify and label the semantics of user queries, playing a vital role in numerous business applications. Despite the dominance of deep learning techniques in this field, the internal mechanisms enabling Recurrent Neural Networks (RNNs) to solve intent detection tasks are poorly understood. In this work, we apply dynamical systems theory to analyze how RNN architectures address this problem, using both the balanced SNIPS and the imbalanced ATIS datasets. By interpreting sentences as trajectories in the hidden state space, we first show that on the balanced SNIPS dataset, the network learns an ideal solution: the state space, constrained to a low-dimensional manifold, is partitioned into distinct clusters corresponding to each intent. The application of this framework to the imbalanced ATIS dataset then reveals how this ideal geometric solution is distorted by class imbalance, causing the clusters for low-frequency intents to degrade. Our framework decouples geometric separation from readout alignment, providing a novel, mechanistic explanation for real world performance disparities. These findings provide new insights into RNN dynamics, offering a geometric interpretation of how dataset properties directly shape a network's computational solution.