systems/arnold_cat_map.json

{
  "system_id": "arnold_cat_map",
  "name": "Arnold's cat map",
  "category": "chaotic",
  "equations": "A linear hyperbolic map on the torus: (x', y') = (2x + y, x + y) mod 1",
  "parameters": {},
  "description_simple": "A linear yet chaotic map on the torus.",
  "description_complex": "Arnold's cat map is a linear toral automorphism that provides one of the cleanest examples of deterministic chaos. Despite its linearity, it exhibits strong sensitivity, mixing, a positive Lyapunov exponent, and Bernoulli dynamics. Crucially, it lacks a strange attractor, breaking the common misconception that nonlinearity is required for chaos.",
  "truth_assignment": {
    "Chaotic": true,
    "Deterministic": true,
    "PosLyap": true,
    "Sensitive": true,
    "StrangeAttr": false,
    "PointUnpredictable": true,
    "StatPredictable": true,
    "QuasiPeriodic": false,
    "Random": false,
    "FixedPointAttr": false,
    "Periodic": false,
    "Dissipative": false,
    "Bounded": true,
    "Mixing": true,
    "Ergodic": true,
    "HyperChaotic": false,
    "Conservative": true,
    "HighDimensional": false,
    "Multifractal": false,
    "HighDimSystem": false,
    "ContinuousTime": false,
    "DiscreteTime": true,
    "DelaySystem": false,
    "Forced": false,
    "Autonomous": true,
    "StrongMixing": true,
    "WeakMixing": true
  }
}