GAIO is a software package for the global numerical analysis of dynamical systems and optimization problems based on set oriented techniques. It may e.g. be used to compute invariant sets, invariant manifolds, invariant measures and almost invariant sets in dynamical systems and to compute the globally optimal solutions of both scalar and multiobjective problems.

References in zbMATH (referenced in 54 articles )

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  1. Froyland, Gary; González-Tokman, Cecilia; Watson, Thomas M.: Optimal mixing enhancement by local perturbation (2016)
  2. Hüls, Thorsten: A contour algorithm for computing stable fiber bundles of nonautonomous, noninvertible maps (2016)
  3. Bittracher, Andreas; Koltai, Péter; Junge, Oliver: Pseudogenerators of spatial transfer operators (2015)
  4. Williams, Matthew O.; Kevrekidis, Ioannis G.; Rowley, Clarence W.: A data-driven approximation of the koopman operator: extending dynamic mode decomposition (2015)
  5. Li, Yongqiang; Hou, Zhongsheng: Data-driven asymptotic stabilization for discrete-time nonlinear systems (2014)
  6. Beyn, Wolf-Jürgen; Lust, Alexander: Error analysis of a hybrid method for computing Lyapunov exponents (2013)
  7. Froyland, Gary; Junge, Oliver; Koltai, Péter: Estimating long-term behavior of flows without trajectory integration: the infinitesimal generator approach (2013)
  8. van den Berg, Jan Bouwe; Day, Sarah; Vandervorst, Robert: Braided connecting orbits in parabolic equations via computational homology (2013)
  9. Castelli, Roberto: Regions of prevalence in the coupled restricted three-body problems approximation (2012)
  10. Flaßkamp, Kathrin; Ober-Blöbaum, Sina; Kobilarov, Marin: Solving optimal control problems by exploiting inherent dynamical systems structures (2012)
  11. Frongillo, Rafael; Treviño, Rodrigo: Efficient automation of index pairs in computational Conley index theory (2012)
  12. Froyland, Gary; Padberg-Gehle, Kathrin: Finite-time entropy: a probabilistic approach for measuring nonlinear stretching (2012)
  13. Collins, Pieter: Semantics and computability of the evolution of hybrid systems (2011)
  14. Horenko, Illia: On analysis of nonstationary categorical data time series: dynamical dimension reduction, model selection, and applications to computational sociology (2011)
  15. Lian, Zeng; Lu, Kening: Lyapunov exponents and invariant manifolds for random dynamical systems in a Banach space (2010)
  16. Wilczak, Daniel: Uniformly hyperbolic attractor of the Smale-Williams type for a Poincaré map in the Kuznetsov system (2010)
  17. Arai, Zin; Kalies, William; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe; Pilarczyk, Paweł: A database schema for the analysis of global dynamics of multiparameter systems (2009)
  18. Beyn, Wolf-Jürgen; Lust, Alexander: A hybrid method for computing Lyapunov exponents (2009)
  19. Dellnitz, Michael; Froyland, Gary; Horenkamp, Christian; Padberg, Kathrin: On the approximation of transport phenomena - a dynamical systems approach (2009)
  20. Froyland, Gary; Padberg, Kathrin: Almost-invariant sets and invariant manifolds - connecting probabilistic and geometric descriptions of coherent structures in flows (2009)

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