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 56 articles )

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  1. Dellnitz, Michael; Klus, Stefan; Ziessler, Adrian: A set-oriented numerical approach for dynamical systems with parameter uncertainty (2017)
  2. Froyland, Gary; González-Tokman, Cecilia; Watson, Thomas M.: Optimal mixing enhancement by local perturbation (2016)
  3. Hüls, Thorsten: A contour algorithm for computing stable fiber bundles of nonautonomous, noninvertible maps (2016)
  4. Schütte, Christof; Koltai, Péter; Klus, Stefan: On the numerical approximation of the Perron-Frobenius and Koopman operator (2016)
  5. Ziessler, Adrian; Hessel-Von Molo, Mirko; Dellnitz, Michael: On the computation of attractors for delay differential equations (2016)
  6. Bittracher, Andreas; Koltai, Péter; Junge, Oliver: Pseudogenerators of spatial transfer operators (2015)
  7. Williams, Matthew O.; Kevrekidis, Ioannis G.; Rowley, Clarence W.: A data-driven approximation of the koopman operator: extending dynamic mode decomposition (2015)
  8. Li, Yongqiang; Hou, Zhongsheng: Data-driven asymptotic stabilization for discrete-time nonlinear systems (2014)
  9. Beyn, Wolf-Jürgen; Lust, Alexander: Error analysis of a hybrid method for computing Lyapunov exponents (2013)
  10. Froyland, Gary; Junge, Oliver; Koltai, Péter: Estimating long-term behavior of flows without trajectory integration: the infinitesimal generator approach (2013)
  11. van den Berg, Jan Bouwe; Day, Sarah; Vandervorst, Robert: Braided connecting orbits in parabolic equations via computational homology (2013)
  12. Castelli, Roberto: Regions of prevalence in the coupled restricted three-body problems approximation (2012)
  13. Flaßkamp, Kathrin; Ober-Blöbaum, Sina; Kobilarov, Marin: Solving optimal control problems by exploiting inherent dynamical systems structures (2012)
  14. Frongillo, Rafael; Treviño, Rodrigo: Efficient automation of index pairs in computational Conley index theory (2012)
  15. Froyland, Gary; Padberg-Gehle, Kathrin: Finite-time entropy: a probabilistic approach for measuring nonlinear stretching (2012)
  16. Collins, Pieter: Semantics and computability of the evolution of hybrid systems (2011)
  17. Horenko, Illia: On analysis of nonstationary categorical data time series: dynamical dimension reduction, model selection, and applications to computational sociology (2011)
  18. Lian, Zeng; Lu, Kening: Lyapunov exponents and invariant manifolds for random dynamical systems in a Banach space (2010)
  19. Wilczak, Daniel: Uniformly hyperbolic attractor of the Smale-Williams type for a Poincaré map in the Kuznetsov system (2010)
  20. 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)

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