GAIO.jl
About
GAIO (Global Analysis of Invariant Objects) is a Julia package for set oriented computations. Sets are represented by collections of boxes. A box (or cube) is a higher dimensional interval, i.e. a set of the form
\[[a_1,b_1) × \ldots × [a_n,b_n), \quad a_k,b_k ∈ ℝ\]
GAIO.jl provides algorithms for
- dynamical systems
- invariant sets (maximal invariant set, chain recurrent set, (relative) attractor, (un-)stable manifold)
- almost invariant and coherent sets
- finite time Lyapunov exponents
- entropy and box dimension
- root finding problems
- multi-objective optimization problems
- computing implicitly defined manifolds
Installation
The package requires Julia 1.10 or later. In Julia's package manager, type
pkg> add https://github.com/gaioguys/GAIO.jl.git
followed by
julia> using GAIO
at the Julia prompt in order to load the package.
Project origin
The package originated as a university seminar for master students in the summer 2020, with the aim to enhance and convert the already existing Matlab GAIO package to Julia.