proposition 32.86 The logistic map at $r=4$ is exactly solvable

open in the book · parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2548 · p. 1110

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proposition 32.86: The logistic map at r=4 is exactly solvable32.86definition 32.73: Lyapunov spectrum32.73equation 32.50: eq:chaos-logistic32.50proof : ch:15-nonlinear-dynamics-chaos@proof-29proofequation 32.45: eq:chaos-variational32.45proposition 32.76: The exponents sum to the mean divergence32.76proposition 32.77: A flow has a zero exponent32.77theorem 32.74: Oseledets, quoted32.74proposition 32.84: Fixed points and the first period doubling32.84

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depends_on Lyapunov spectrum declared parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2556
depends_on eq:chaos-logistic declared parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2556
proves ch:15-nonlinear-dynamics-chaos@proof-29 declared parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:2559