Global Analysis of Invariant Objects

• the setwise approximation of invariant sets like (relative) global attractors, invariant manifolds of (in principle) arbitrary dimension [1,2];
• the approximation of natural invariant measures [3,4].

In forthcoming versions it will additionally be possible to approximate cyclic behavior and to identify "almost invariant sets" [4,5].

GAIO can no longer be downloaded. If you wish to obtain it, you should contact the developers at gaio@math.uni-paderborn.de. GAIO has its own homepage where you can find information on how to use it.

Contact person for GAIO is Michael Dellnitz ( dellnitz@math.uni-paderborn.de)

References

1. M. Dellnitz and A. Hohmann
   A subdivision algorithm for the computation of unstable manifolds and global attractors
   Num. Math. 75 : 293-317, 1997.
2. M. Dellnitz and A. Hohmann
   "The computation of unstable manifolds using subdivision and continuation"
   in H.W. Broer et al. (Eds.) Progress in Nonlinear Differential Equations and Their Applications 19: 449-459, Birkhäuser Verlag, Basel / Switzerland, 1996.
3. Michael Dellnitz, Andreas Hohmann, Oliver Junge, and Martin Rumpf
   Exploring invariant sets and invariant measures
   CHAOS 7(2) : 221-228, 1997.
4. Dellnitz, Michael; Junge, Oliver
   On the approximation of complicated dynamical behavior
   SIAM Journal on Numerical Analysis 36(2) : 491-515, 1999.
5. Dellnitz, Michael; Junge, Oliver
   Almost invariant sets in Chua's circuit
   Int. J. Bifurcation & Chaos 7(11) : 2475-2485, 1997.