Computing the Lyapunov exponent of the Hénon map with DynamicalSystems.jl

Specific Domains Modelling & Simulations
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2

Hi,

  1. What does “converge” mean?
  2. upper_threshold = 1e-4. Lyapunov exponents are in theory defined for infinitesimal perturbations. You want Δt and threshold to be such that perturbation growth is limited to linearized dynamics. Is this true here?
  3. What is the trajectory of the dynamical system doing for these parameters?

I see:

julia> tr = trajectory(henon, 100; Ttr = 1000)
2-dimensional Dataset{Float64} with 101 points
 -Inf  -Inf
 -Inf  -Inf
 -Inf  -Inf
 -Inf  -Inf
 -Inf  -Inf
 -Inf  -Inf
 -Inf  -Inf
 -Inf  -Inf
 -Inf  -Inf
 -Inf  -Inf
   ⋮
 -Inf  -Inf
 -Inf  -Inf
 -Inf  -Inf
 -Inf  -Inf
 -Inf  -Inf
 -Inf  -Inf
 -Inf  -Inf
 -Inf  -Inf
 -Inf  -Inf

the system goes to infinity for a=1.75…

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