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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.