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    Home/Original/inverse
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    Inverse View

    It is not the case that Global Lyapunov exponents may lack physical significance for real-world systems

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Global Lyapunov exponents only apply to infinitesimal uncertainties
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    • 2.Uncertainties in physical systems are always larger than infinitesimal
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    • 3.Any growth in uncertainties between neighboring trajectories can be fitted with an exponential function
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Global Lyapunov exponents are computed as time-averages over infinite trajectories, but physically realizable observations are always finite-duration.
      ?

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    • 2.Eckmann and Ruelle (1985) acknowledge that ergodic theory's infinite-time limits need not converge to physically observable rates on measurable timescales.
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    • 3.A quantity defined only in an idealized infinite limit cannot straightforwardly characterize the finite-time behavior of systems embedded in physical reality.
      ?

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    Reason against 2 of 2
    ?
    • 1.Suppes and Winsberg's arguments on model-world gaps entail that mathematical invariants of abstract systems need not correspond to measurable physical quantities.
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    • 2.The Lyapunov exponent presupposes a fixed, smooth invariant measure, but real systems subject to noise and perturbation do not preserve such measures exactly.
      ?

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    • 3.When the theoretical preconditions of a formal quantity fail to obtain in target physical systems, that quantity loses its claim to physical significance.
      ?

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