Is there an example of a system with "oscillating" sets, ie sets with eigenvalue -1 for the TransferOperator? I know the Lorenz system would work, but we already used that so it might be nice to have a new system.
With this system we can calculate a BoxFun with eigenvalue -1 and write:
(lambda, ev) = eigs(T; which=:SR) # get ev with smallest real part ":SR", should be -1
μ = ev[1]
μ_categorical = >(0) ∘ real ∘ μ # split μ into positive and negative real parts
plot(μ_categorical) # two sets that "oscillate" between each other
Tμ = T * μ
Tμ_categorical = >(0) ∘ real ∘ Tμ
plot(Tμ_categorical) # we see the two sets "swap"
April-Hannah-Lena
commented
1 year ago
Is there an example of a system with "oscillating" sets, ie sets with eigenvalue -1 for the TransferOperator? I know the Lorenz system would work, but we already used that so it might be nice to have a new system.
With this system we can calculate a BoxFun with eigenvalue -1 and write: