Chaos Lab

Discrete map · 1D · dim 1

Sine map

Topologically equivalent to the logistic in the chaotic regime; the smoothness changes critical exponents in transient analysis. Common in studies of period-doubling universality.

Bifurcation diagram of x ↦ a·sin(π x), a ∈ [0.7, 1]. Same universality class as logistic.

Equations

x_{n+1} = a · sin(π x_n)

At a glance

Parametersa ∈ (0, 1]
Chaotic fora close to 1 (a > a∞ ≈ 0.86)
Lyapunov exponentvaries with a
HistoryFeigenbaum's universality calculations used this map as a smoothness check.

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See also

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