GAIO swMATH ID: 4306 Software Authors: djs2 GmbH; Dellnitz, Michael; Froyland, Gary; Junge, Oliver Description: 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. Homepage: https://www2.math.uni-paderborn.de/ags/ag-dellnitz/software.html Related Software: Matlab; AUTO; ARPACK; CAPD; VAMPnets; EnKF; SCS; PRMLT; CHomP; Scotch; PROFIL/BIAS; C-XSC 2.0; ns-2; Chom; Homology; odmd; DeepONet; PyDMD; rsvd; COCO Cited in: 95 Publications Further Publications: http://math-www.uni-paderborn.de/AG/Dellnitz/index_publications.html Standard Articles 2 Publications describing the Software, including 2 Publications in zbMATH Year Set oriented numerical methods for dynamical systems. Zbl 1036.37030Dellnitz, Michael; Junge, Oliver 2002 The algorithms behind GAIO – set oriented numerical methods for dynamical systems. Zbl 0998.65126Dellnitz, Michael; Froyland, Gary; Junge, Oliver 2001 all top 5 Cited by 154 Authors 13 Dellnitz, Michael 12 Junge, Oliver 10 Froyland, Gary 9 Padberg-Gehle, Kathrin 5 Giesl, Peter 5 Hafstein, Sigurður Freyr 5 Koltai, Péter 5 Ziessler, Adrian 4 Day, Sarah L. 4 Klus, Stefan 4 Mischaikow, Konstantin 3 Argaez, Carlos 3 Collins, Peter J. 3 González-Tokman, Cecilia 3 Kevrekidis, Ioannis George 3 Marsden, Jerrold Eldon 3 Rasmussen, Martin 3 Ross, Shane D. 3 Siegmund, Stefan 3 Thiere, Bianca 3 Vandervorst, Robertus C. A. M. 2 Aulbach, Bernd 2 Beyn, Wolf-Jürgen 2 Castelli, Roberto 2 Elamvazhuthi, Karthik 2 Flaßkamp, Kathrin 2 Frongillo, Rafael M. 2 Gerlach, Raphael 2 Grover, Piyush 2 Hessel-von Molo, Mirko 2 Imkeller, Peter 2 Kalies, William D. 2 Kokubu, Hiroshi 2 Lust, Alexander 2 Osinga, Hinke Maria 2 Pilarczyk, Paweł 2 Preis, Robert 2 Rowley, Clarence W. 2 Schütte, Christof 2 Treviño, Rodrigo 2 van den Berg, Jan Bouwe 2 Williams, Matthew O. 1 Alpcan, Tansu 1 Ansari, Alex R. 1 Arai, Zin 1 Arnold, Ludwig 1 Avrutin, Viktor 1 Baier, Robert 1 Bánhelyi, Balázs 1 Barke, Erich 1 Başar, Tamer 1 Berger, Arno 1 Bittracher, Andreas 1 Björnsson, Jóhann 1 Blachut, Chantelle 1 Bollt, Erik M. 1 Broer, Henk W. 1 Brunton, Steven L. 1 Budišić, Marko 1 Chandrasekaran, Shivkumar 1 Chekroun, Mickaël D. 1 Colonius, Fritz 1 Csendes, Tibor 1 Denner, Andreas 1 Dijkstra, Henk A. 1 Doedel, Eusebius J. 1 Eckhardt, Bruno 1 Fiedler, Bernold 1 Fundinger, Danny 1 Garay, Barnabas M. 1 Govindarajan, Nithin 1 Graça, Daniel Silva 1 Grubits, K. A. 1 Grüne, Lars 1 Guckenheimer, John M. 1 Hagen, Aaron 1 Hartong, Walter 1 Hatvani, László 1 Hedrich, Lars 1 Henderson, Michael E. 1 Horenkamp, Christian 1 Horenko, Illia 1 Hou, Zhongsheng 1 Hüls, Thorsten 1 Inatsu, Masaru 1 Oertel-Jäger, Tobias Hendrik 1 Kaiser, Eurika 1 Kellett, Christopher M. 1 Kloeden, Peter Eris 1 Klünker, Anna 1 Kobilarov, Marin 1 Kong, Chen 1 Koon, Wang Sang 1 Krauskopf, Bernd 1 Kreuzer, Edwin J. 1 Kutz, J. Nathan 1 Langhorne, Zachary 1 Lekien, Francois 1 Li, Yongqiang 1 Lian, Zeng ...and 54 more Authors all top 5 Cited in 40 Serials 12 SIAM Journal on Applied Dynamical Systems 9 Journal of Computational Dynamics 6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 4 Numerische Mathematik 4 Physica D 4 Communications in Nonlinear Science and Numerical Simulation 3 Journal of Nonlinear Science 3 Nonlinear Dynamics 3 Discrete and Continuous Dynamical Systems. Series B 2 Nonlinearity 2 SIAM Journal on Numerical Analysis 2 SIAM Review 2 Discrete and Continuous Dynamical Systems 2 Chaos 1 Computers & Mathematics with Applications 1 Journal of Statistical Physics 1 Mathematics of Computation 1 Automatica 1 Journal of Differential Equations 1 Memoirs of the American Mathematical Society 1 SIAM Journal on Control and Optimization 1 Theoretical Computer Science 1 Transactions of the American Mathematical Society 1 Topology and its Applications 1 Ergodic Theory and Dynamical Systems 1 Systems & Control Letters 1 Bulletin of the American Mathematical Society. New Series 1 Celestial Mechanics and Dynamical Astronomy 1 Journal of Dynamics and Differential Equations 1 Journal of Vibration and Control 1 Theory of Computing Systems 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Regular and Chaotic Dynamics 1 Dynamical Systems 1 Foundations of Computational Mathematics 1 Stochastics and Dynamics 1 Multiscale Modeling & Simulation 1 Acta Numerica 1 GAMM-Mitteilungen 1 Nonlinear Analysis. Hybrid Systems all top 5 Cited in 27 Fields 70 Dynamical systems and ergodic theory (37-XX) 30 Numerical analysis (65-XX) 15 Ordinary differential equations (34-XX) 11 Systems theory; control (93-XX) 10 Mechanics of particles and systems (70-XX) 8 Fluid mechanics (76-XX) 7 Operator theory (47-XX) 6 Probability theory and stochastic processes (60-XX) 5 Partial differential equations (35-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Statistical mechanics, structure of matter (82-XX) 4 Geophysics (86-XX) 4 Operations research, mathematical programming (90-XX) 3 Statistics (62-XX) 3 Computer science (68-XX) 2 Mathematical logic and foundations (03-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Difference and functional equations (39-XX) 1 General and overarching topics; collections (00-XX) 1 Measure and integration (28-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX) 1 Astronomy and astrophysics (85-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX) Citations by Year