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 94 articles , 2 standard articles )

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  1. Brunton, Steven L.; Budišić, Marko; Kaiser, Eurika; Kutz, J. Nathan: Modern Koopman theory for dynamical systems (2022)
  2. Giesl, Peter; Argáez, Carlos; Hafstein, Sigurdur; Wendland, Holger: Minimization with differential inequality constraints applied to complete Lyapunov functions (2021)
  3. Giesl, Peter; Langhorne, Zachary; Argáez, Carlos; Hafstein, Sigurdur: Computing complete Lyapunov functions for discrete-time dynamical systems (2021)
  4. Blachut, Chantelle; González-Tokman, Cecilia: A tale of two vortices: how numerical ergodic theory and transfer operators reveal fundamental changes to coherent structures in non-autonomous dynamical systems (2020)
  5. Chekroun, Mickaël D.; Tantet, Alexis; Dijkstra, Henk A.; Neelin, J. David: Ruelle-Pollicott resonances of stochastic systems in reduced state space. Part I: Theory (2020)
  6. Gerlach, Raphael; Ziessler, Adrian: The approximation of invariant sets in infinite dimensional dynamical systems (2020)
  7. Gerlach, Raphael; Ziessler, Adrian; Eckhardt, Bruno; Dellnitz, Michael: A set-oriented path following method for the approximation of parameter dependent attractors (2020)
  8. Grüne, Lars; Junge, Oliver: From Bellman to Dijkstra: set-oriented construction of globally optimal controllers (2020)
  9. Klünker, Anna; Schneide, Christiane; Froyland, Gary; Schumacher, Jörg; Padberg-Gehle, Kathrin: Set-oriented and finite-element study of coherent behavior in Rayleigh-Bénard convection (2020)
  10. Koltai, Péter; Weiss, Stephan: Diffusion maps embedding and transition matrix analysis of the large-scale flow structure in turbulent Rayleigh-Bénard convection (2020)
  11. Santitissadeekorn, Naratip; Bollt, Erik M.: Ensemble-based method for the inverse Frobenius-Perron operator problem: data-driven global analysis from spatiotemporal “movie” data (2020)
  12. Wu, Hao; Noé, Frank: Variational approach for learning Markov processes from time series data (2020)
  13. Froyland, Gary; González-Tokman, Cecilia; Murray, Rua: Quenched stochastic stability for eventually expanding-on-average random interval map cocycles (2019)
  14. Govindarajan, Nithin; Mohr, Ryan; Chandrasekaran, Shivkumar; Mezic, Igor: On the approximation of Koopman spectra for measure preserving transformations (2019)
  15. Morita, Hidetoshi; Inatsu, Masaru; Kokubu, Hiroshi: Topological computation analysis of meteorological time-series data (2019)
  16. Nave, Gary K. jun.; Nolan, Peter J.; Ross, Shane D.: Trajectory-free approximation of phase space structures using the trajectory divergence rate (2019)
  17. Sahai, Tuhin; Ziessler, Adrian; Klus, Stefan; Dellnitz, Michael: Continuous relaxations for the traveling salesman problem (2019)
  18. Wormell, Caroline: Spectral Galerkin methods for transfer operators in uniformly expanding dynamics (2019)
  19. Yue, Xiao-Le; Xu, Yong; Xu, Wei; Sun, Jian-Qiao: Global invariant manifolds of dynamical systems with the compatible cell mapping method (2019)
  20. Argáez, Carlos; Giesl, Peter; Hafstein, Sigurdur Freyr: Computational approach for complete Lyapunov functions (2018)

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