Ergodic

physicsstatistical mechanicsdynamical systemsergodicityphase spacechaos theorytrajectoriescetztikz

Phase space diagram showing two types of trajectories in a 2D oscillator system: a non-ergodic trajectory R (in red) for rational frequency ratio ω = 2 which forms a closed orbit, and an ergodic region R (in orange) for irrational frequency ratio ω ∉ ℚ which densely fills the available phase space P (blue ellipse). The diagram illustrates how ergodicity depends on the rationality of frequency ratios.