<p>We study the dynamical behavior of discrete Lotka–Volterra operators acting on the three-dimensional simplex. The structure of invariant sets, including fixed points and regions determining the direction of trajectories, is analyzed by means of the Jacobian spectrum and suitably constructed Lyapunov functions. Using LaSalle’s invariance principle, trajectories are shown to converge to invariant sets under suitable conditions. A notion of trajectory signatures is introduced, providing a classification of dynamical regimes and a geometric description of trajectory routing inside the simplex. The combination of signature-based analysis and Lyapunov methods yields a unified framework for investigating the dynamics of degenerate Lotka–Volterra mappings. Numerical examples based on Lyapunov-function optimization are presented to support the theoretical results.</p>