This phenomenon is not possible in planar, finite, continuous dynamics due to the Poincaré–Bendixson theorem. Given mixing and density properties, it corresponds to a Lyapunov exponent with positive real part because it is typified by exponential divergence in time of initially close trajectories. The long-time behavior of all trajectories in systems exhibiting this behavior is typified by fractals to which all points in state space converge, ter
This phenomenon is not possible in planar, finite, continuous dynamics due to the Poincaré–Bendixson theorem. Given mixing and density properties, it corresponds to a Lyapunov exponent with positive real part because it is typified by exponential divergence in time of initially close trajectories. The long-time behavior of all trajectories in systems exhibiting this behavior is typified by fractals to which all points in state space converge, termed strange attractors. Partially arising due to the butterfly effect, for 10 points, name this type of behavior which is deterministic but difficult to predict, in contrast with stochastic behavior.
This phenomenon is not possible in planar, finite, continuous dynamics due to the Poincaré–Bendixson theorem.
deterministic {chaos} [prompt on {butterfly effect} or clear-knowledge equivalents before it's mentioned]