Issue
I am trying to compute the Lyapunov exponent of the Hénon map with b = 0.3
and a = 1.8
but the lyapunov
function from DynamicalSystems.jl
seems to not converge. Is there something I am doing wrong or is this expected?
Minimal working example
This does not converge:
using DynamicalSystems
henon = Systems.henon(a = 1.75)
λ = lyapunov(henon, 10000, d0 = 1e7, upper_threshold = 1e4, Ttr = 100)
This converges very quickly:
henon = Systems.henon(a = 1.)
λ = lyapunov(henon, 10000, d0 = 1e7, upper_threshold = 1e4, Ttr = 100)
Hi,
 What does “converge” mean?

upper_threshold = 1e4
. 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?
 What is the trajectory of the dynamical system doing for these parameters?
I see:
julia> tr = trajectory(henon, 100; Ttr = 1000)
2dimensional 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
…
1 Like
Thank you for the quick reply! You are indeed correct, I did not realise the trajectory was diverging for a = 1.75
.