Deterministic Nonperiodic Flow.¶
Lorenz, E. N. (1963). Deterministic Nonperiodic Flow. Journal of the Atmospheric Sciences, 20(2), 130-141.
Cited by¶
10 citations across 10 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Chaos
- In mathematics, chaos is studied through iterated maps (logistic map, Hénon map, baker's map), continuous chaotic systems (Lorenz
This sourceDerives the Lorenz equations by truncating Saltzman's convection model to three modes; discovers the Lorenz strange attractor exhibiting sensitive dependence on initial conditions; foundational for chaos theory.
- In mathematics, chaos is studied through iterated maps (logistic map, Hénon map, baker's map), continuous chaotic systems (Lorenz
- Convection
- The Lorenz equations derived from a truncation of convection dynamics exhibit the Lorenz attractor, a hallmark of chaos in nonlinear systems
This sourceDerives a three-mode truncation of a cellular-convection model (after Saltzman) and discovers the Lorenz attractor — deterministic chaos with sensitive dependence on initial conditions.
- The Lorenz equations derived from a truncation of convection dynamics exhibit the Lorenz attractor, a hallmark of chaos in nonlinear systems
- Determinism
- A chaotic dynamical system (the canonical example: the Lorenz attractor or a double pendulum) is deterministic at every step (state plus equations of motion fix the next state uniquely) yet practically unpredictable beyond a short horizon, because vanishingly small errors in measured state grow exponentially — the result Lorenz (1963) established in his foundational paper on deterministic nonperiodic flow.
This sourceDerives the three-mode Lorenz equations from a convection model, discovers the strange (Lorenz) attractor exhibiting sensitive dependence on initial conditions, and establishes deterministic chaos — the foundational result that a deterministic system can be practically unpredictable (080).
- A chaotic dynamical system (the canonical example: the Lorenz attractor or a double pendulum) is deterministic at every step (state plus equations of motion fix the next state uniquely) yet practically unpredictable beyond a short horizon, because vanishingly small errors in measured state grow exponentially — the result Lorenz (1963) established in his foundational paper on deterministic nonperiodic flow.
- Foreseeing (Prediction)
- The chaos theory perspective
This sourceIntroduces the three-mode Lorenz system and sensitive dependence on initial conditions (the 'butterfly effect'); supports the T4 claim that deterministic systems can be unpredictable at long horizons because initial-condition uncertainty grows exponentially.
- The chaos theory perspective
- Perturbation
- See Instability. Not chaos. Chaos is a regime of exponential divergence of nearby trajectories; small perturbations are the probe that reveals chaos (Lyapunov exponents), but chaos is the system property.
This sourceDerives the Lorenz equations by further truncating Saltzman's convection model to three modes; discovers the Lorenz attractor, a strange attractor exhibiting sensitive dependence on initial conditions and deterministic chaos; foundational for chaos theory and demonstrating that a physical system (convection) exhibits chaotic behavior. Lorenz attractor, three-mode truncation, deterministic chaos, sensitivity to initial conditions.
- See Instability. Not chaos. Chaos is a regime of exponential divergence of nearby trajectories; small perturbations are the probe that reveals chaos (Lyapunov exponents), but chaos is the system property.
- Randomness
- Every randomness claim names (1) the process generating the outcomes, (2) the reference scheme against which unpredictability is asserted (no pattern recoverable by this class of methods), (3) the statistical regularities that do hold (a distribution, a stationarity property, an exchangeability condition), and (4) the source of the unpredictability — fundamental indeterminism (aleatoric), deterministic
chaosin the sense of Lorenz (1963)This sourceDerives the Lorenz equations by further truncating Saltzman's convection model to three modes; discovers the Lorenz attractor, a strange attractor exhibiting sensitive dependence on initial conditions and deterministic chaos; foundational for chaos theory and demonstrating that a physical system (convection) exhibits chaotic behavior. Lorenz attractor, three-mode truncation, deterministic chaos, sensitivity to initial conditions.
- Every randomness claim names (1) the process generating the outcomes, (2) the reference scheme against which unpredictability is asserted (no pattern recoverable by this class of methods), (3) the statistical regularities that do hold (a distribution, a stationarity property, an exchangeability condition), and (4) the source of the unpredictability — fundamental indeterminism (aleatoric), deterministic
- Recurrence
- "Can we reach a fixed point, or are we destined to oscillate?"—the family of questions Lorenz (1963) opened when he showed that deterministic recurrence relations can amplify infinitesimal differences in initial conditions into wholly different long-term trajectories.
This sourceDerives the Lorenz equations by further truncating Saltzman's convection model to three modes; discovers the Lorenz attractor, a strange attractor exhibiting sensitive dependence on initial conditions and deterministic chaos; foundational for chaos theory and demonstrating that a physical system (convection) exhibits chaotic behavior. Lorenz attractor, three-mode truncation, deterministic chaos, sensitivity to initial conditions.
- "Can we reach a fixed point, or are we destined to oscillate?"—the family of questions Lorenz (1963) opened when he showed that deterministic recurrence relations can amplify infinitesimal differences in initial conditions into wholly different long-term trajectories.
- Self-Organized Criticality
- Large-scale weather patterns (monsoons, hurricanes, jet streams) emerge from chaotic interactions of millions of molecules governed by local thermodynamic laws, a sensitivity to fine-scale fluctuations Lorenz (1963) exposed in his discovery of deterministic nonperiodic flow underlying atmospheric dynamics.
This sourceDerives the Lorenz equations by further truncating Saltzman's convection model to three modes; discovers the Lorenz attractor, a strange attractor exhibiting sensitive dependence on initial conditions and deterministic chaos; foundational for chaos theory and demonstrating that a physical system (convection) exhibits chaotic behavior. Lorenz attractor, three-mode truncation, deterministic chaos, sensitivity to initial conditions.
- Large-scale weather patterns (monsoons, hurricanes, jet streams) emerge from chaotic interactions of millions of molecules governed by local thermodynamic laws, a sensitivity to fine-scale fluctuations Lorenz (1963) exposed in his discovery of deterministic nonperiodic flow underlying atmospheric dynamics.
- Stochasticity vs. Determinism
- A chaotic system obeys deterministic laws—given perfect knowledge of initial conditions, the future is fully specified—but the exquisite sensitivity to initial conditions means that any real measurement error grows exponentially, rendering prediction useless in practice—a phenomenon Lorenz (1963) demonstrated in his foundational study of nonperiodic flow.
This sourceDerives the Lorenz equations by further truncating Saltzman's convection model to three modes; discovers the Lorenz attractor, a strange attractor exhibiting sensitive dependence on initial conditions and deterministic chaos; foundational for chaos theory and demonstrating that a physical system (convection) exhibits chaotic behavior. Lorenz attractor, three-mode truncation, deterministic chaos, sensitivity to initial conditions.
- A chaotic system obeys deterministic laws—given perfect knowledge of initial conditions, the future is fully specified—but the exquisite sensitivity to initial conditions means that any real measurement error grows exponentially, rendering prediction useless in practice—a phenomenon Lorenz (1963) demonstrated in his foundational study of nonperiodic flow.
Domain-specific¶
Verification¶
Does it exist? Not confirmed. The DOI recorded for this work did not resolve when it was last checked, so it is shown above but not linked. The citation may still be sound; the recorded identifier is not. Flagged for repair.
Does it back the claim? Not recorded. Neither this nor any other of the 10 citations of this work carries a recorded support check.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Links previously used in the corpus¶
Before the registry existed this work was also linked 2 other ways.
- https://doi.org/10.1175/1520-0469(1963)020%3C0130:DNF%3E2.0.CO;2 ×3
- https://samizdat.co/works/do-while/lorenz-1963.pdf ×1
Registry ID ref:91cb4292eb25 · see in the full table