Hyperbolic toral automorphisms are a class of dynamical systems that arise from transformations on the torus where at least one of the eigenvalues of the transformation matrix is greater than one and at least one is less than one, creating an expanding and contracting behavior. This unique property results in chaotic behavior, making these systems important examples of mixing systems in ergodic theory, showcasing how orbits can spread out uniformly over the torus.
congrats on reading the definition of hyperbolic toral automorphisms. now let's actually learn it.