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Biasco, L., &; Di Gregorio, L. (2009). A Birkhoff–Lewis Type Theorem for the Nonlinear Wave Equation. Archive for Rational Mechanics and Analysis, 303–362.https://doi.org/10.1007/s00205-009-0240-y 

Eckstein, J., Peitz, S., Schäfer, K., Friedel, P., Köhler, U., Hessel von Molo, M., Ober-Blöbaum, S., &; Dellnitz, M. (2016). A comparison of two predictive approaches to control the longitudinal dynamics of electric vehicles. Procedia Technology, 3rd International Conference on System-Integrated Intelligence: New Challenges for Product and Production Engineering, 26, 465–472.https://doi.org/10.1016/j.protcy.2016.08.059 

Dellnitz, M., Froyland, G., &; Sertl, S. (2000). A Conjecture on the Existence of Isolated Eigenvalues of the Perron-Frobenius Operator. In Equadiff 99.https://doi.org/10.1142/9789812792617_0199 

Gebken, B., Peitz, S., &; Dellnitz, M. (2018). A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems. In Numerical and Evolutionary Optimization – NEO 2017. Cham.https://doi.org/10.1007/978-3-319-96104-0_2 

Sonntag, K., Gebken, B., Müller, G., Peitz, S., &; Volkwein, S. (2024). A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces. In arXiv:2402.06376.

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Dellnitz, M., Ober-Blöbaum, S., Post, M., Schütze, O., &; Thiere, B. (2009). A multi-objective approach to the design of low thrust space trajectories using optimal control. Celestial Mechanics and Dynamical Astronomy, 33–59.https://doi.org/10.1007/s10569-009-9229-y 

Peitz, S., Schäfer, K., Ober-Blöbaum, S., Eckstein, J., Köhler, U., &; Dellnitz, M. (2017). A multiobjective MPC approach for autonomously driven electric vehicles. Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC), 50(1), 8674–8679.https://doi.org/10.1016/j.ifacol.2017.08.1526 

Peitz, S., Schäfer, K., Ober-Blöbaum, S., Eckstein, J., Köhler, U., &; Dellnitz, M. (2017). A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This research was funded by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe (it’s OWL). IFAC-PapersOnLine, 8674–8679.https://doi.org/10.1016/j.ifacol.2017.08.1526 

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Witting, K., Schulz, B., Dellnitz, M., Böcker, J., &; Fröhleke, N. (2008). A new approach for online multiobjective optimization of mechatronic systems. International Journal on Software Tools for Technology Transfer, 223–231.https://doi.org/10.1007/s10009-008-0066-1 

Schütze, O. (2003). A New Data Structure for the Nondominance Problem in Multi-objective Optimization. In Lecture Notes in Computer Science. Berlin, Heidelberg.https://doi.org/10.1007/3-540-36970-8_36 

Gebken, B. (2024). A note on the convergence of deterministic gradient sampling in nonsmooth optimization. Computational Optimization and Applications.https://doi.org/10.1007/s10589-024-00552-0 

Dellnitz, M., &; Melbourne, I. (1995). A note on the shadowing lemma and symmetric periodic points. Nonlinearity, 1067–1075.https://doi.org/10.1088/0951-7715/8/6/010 

von der Gracht, S., Nijholt, E., &; Rink, B. (n.d.). A parametrisation method for high-order phase reduction in coupled  oscillator networks. In arXiv:2306.03320.

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Grüne, L., &; Junge, O. (2005). A set oriented approach to optimal feedback stabilization. Systems &; Control Letters, 169–180.https://doi.org/10.1016/j.sysconle.2004.08.005 

Dellnitz, M., Klus, S., &; Ziessler, A. (2017). A Set-Oriented Numerical Approach for Dynamical Systems with Parameter Uncertainty. SIAM Journal on Applied Dynamical Systems, 120–138.https://doi.org/10.1137/16m1072735 

Gerlach, R., Ziessler, A., Eckhardt, B., &; Dellnitz, M. (2020). A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors. SIAM Journal on Applied Dynamical Systems, 705–723.https://doi.org/10.1137/19m1247139 

Dellnitz, M., &; Hohmann, A. (1997). A subdivision algorithm for the computation of unstable manifolds and global attractors. Numerische Mathematik, 75, 293–317.https://doi.org/10.1007/s002110050240 

Krauskopf, B., Osinga, H. M., Doedel, E. J., Henderson, M. E., Guckenheimer, J., Vladimirsky, A.,https://doi.org/10.1142/s0218127405012533__Junge, O. (2005). A Survey of Methods for Computing (un)stable Manifolds of Vector Fields. International Journal of Bifurcation and Chaos, 763–791.https://doi.org/10.1142/s0218127405012533 

Peitz, S., &; Dellnitz, M. (2018). A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction. Mathematical and Computational Applications, 23(2).https://doi.org/10.3390/mca23020030 

Witting, K., Ober-Blöbaum, S., &; Dellnitz, M. (2013). A variational approach to define robustness for parametric multiobjective optimization problems. Journal of Global Optimization, 331–345.https://doi.org/10.1007/s10898-012-9972-6 

Noé, F., &; Nüske, F. (2013). A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems. Multiscale Modeling &; Simulation, 635–655.https://doi.org/10.1137/110858616 

Dellnitz, M., &; Heinrich, C. (1995). Admissible symmetry increasing bifurcations. Nonlinearity, 1039–1066.https://doi.org/10.1088/0951-7715/8/6/009 

Vieluf, S., Mora, K., Gölz, C., Reuter, E.-M., Godde, B., Dellnitz, M.,https://doi.org/10.1016/j.neuroscience.2018.07.025__Voelcker-Rehage, C. (2018). Age- and Expertise-Related Differences of Sensorimotor Network Dynamics during Force Control. Neuroscience, 203–213.https://doi.org/10.1016/j.neuroscience.2018.07.025 

Dellnitz, M., &; Junge, O. (1997). Almost Invariant Sets in Chua’s Circuit. International Journal of Bifurcation and Chaos, 2475–2485.https://doi.org/10.1142/s0218127497001655 

Guder, R., Dellnitz, M., &; Kreuzer, E. (1997). An adaptive method for the approximation of the generalized cell mapping. Chaos, Solitons &; Fractals, 525–534.https://doi.org/10.1016/s0960-0779(96)00118-x 

Dellnitz, M., &; Junge, O. (1998). An adaptive subdivision technique for the approximation of attractors and invariant measures. Computing and Visualization in Science, 63–68.https://doi.org/10.1007/s007910050006 

Junge, O. (2001). An adaptive subdivision technique for the approximation of attractors and invariant measures: proof of convergence. Dynamical Systems, 213–222.https://doi.org/10.1080/14689360109696233 

Klus, S., Sahai, T., Liu, C., &; Dellnitz, M. (2011). An efficient algorithm for the parallel solution of high-dimensional differential equations. Journal of Computational and Applied Mathematics, 3053–3062.https://doi.org/10.1016/j.cam.2010.12.026 

Gebken, B., &; Peitz, S. (2021). An efficient descent method for locally Lipschitz multiobjective optimization problems. Journal of Optimization Theory and Applications, 188, 696–723.https://doi.org/10.1007/s10957-020-01803-w 

Timmermann, R., &; Dellnitz, M. (2013). Analysis of team and player performance using recorded trajectory data. In Performance Analysis of Sport IX, Part 8, Routledge.

Klus, S., Peitz, S., &; Schuster, I. (2018). Analyzing high-dimensional time-series data using kernel transfer  operator eigenfunctions. ArXiv:1805.10118.

Preis, R., Monien, B., &; Schamberger, S. (2007). Approximation Algorithms for Multilevel Graph Partitioning. In Handbook of Approximation Algorithms and Metaheuristics.https://doi.org/10.1201/9781420010749.ch60 

Demoures, F., Gay-Balmaz, F., Leitz, T., Leyendecker, S., Ober-Blöbaum, S., &; Ratiu, T. S. (2013). Asynchronous variational Lie group integration for geometrically exact beam dynamics. PAMM, 45–46.https://doi.org/10.1002/pamm.201310018 

Nüske, F., Boninsegna, L., &; Clementi, C. (2019). Coarse-graining molecular systems by spectral matching. The Journal of Chemical Physics.https://doi.org/10.1063/1.5100131 

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Gebken, B. (2022). Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization.https://doi.org/10.17619/UNIPB/1-1327 

Deuflhard, P., Dellnitz, M., Junge, O., &; Schütte, C. (1999). Computation of Essential Molecular Dynamics by Subdivision Techniques. In Computational Molecular Dynamics: Challenges, Methods, Ideas. Berlin, Heidelberg.https://doi.org/10.1007/978-3-642-58360-5_5 

Dellnitz, M., &; Witting, K. (2009). Computation of robust Pareto points. International Journal of Computing Science and Mathematics.https://doi.org/10.1504/ijcsm.2009.027876 

Aston, P. J., &; Dellnitz, M. (2003). Computation of the dominant Lyapunov exponent via spatial integration using matrix norms. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2933–2955.https://doi.org/10.1098/rspa.2003.1143 

Dellnitz, M. (1992). Computational bifurcation of periodic solutions in systems with symmetry. IMA Journal of Numerical Analysis, 12(3), 429–455.https://doi.org/10.1093/imanum/12.3.429 

Dellnitz, M., &; Werner, B. (1989). Computational methods for bifurcation problems with symmetries—with special attention to steady state and Hopf bifurcation points. Journal of Computational and Applied Mathematics, 97–123.https://doi.org/10.1016/0377-0427(89)90150-7 

Gail, T., Leyendecker, S., &; Ober-Blöbaum, S. (2013). Computing time investigations for variational multirate integration. PAMM, 43–44.https://doi.org/10.1002/pamm.201310017 

Dellnitz, M., &; Preis, R. (2003). Congestion and Almost Invariant Sets in Dynamical Systems. In Lecture Notes in Computer Science. Berlin, Heidelberg.https://doi.org/10.1007/3-540-45084-x_8 

Dellnitz, M., Padberg, K., Preis, R., &; Thiere, B. (2010). Continuous and Discrete Concepts for Detecting Transport Barriers in the Planar Circular Restricted Three Body Problem. In Nonlinear Science and Complexity. Dordrecht.https://doi.org/10.1007/978-90-481-9884-9_12 

Sahai, T., Ziessler, A., Klus, S., &; Dellnitz, M. (2019). Continuous relaxations for the traveling salesman problem. Nonlinear Dynamics.https://doi.org/10.1007/s11071-019-05092-5 

Flaßkamp, K., Timmermann, J., Ober-Blöbaum, S., &; Trächtler, A. (2014). Control strategies on stable manifolds for energy-efficient swing-ups of double pendula. International Journal of Control, 1886–1905.https://doi.org/10.1080/00207179.2014.893450 

Peitz, S. (2018). Controlling nonlinear PDEs using low-dimensional bilinear approximations  obtained from data. ArXiv:1801.06419.

Schütze, O., Laumanns, M., Coello Coello, C. A., Dellnitz, M., &; Talbi, E.-G. (2008). Convergence of stochastic search algorithms to finite size pareto set approximations. Journal of Global Optimization, 559–577.https://doi.org/10.1007/s10898-007-9265-7 

Schütze, O., Mostaghim, S., Dellnitz, M., &; Teich, J. (2003). Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques. In Lecture Notes in Computer Science. Berlin, Heidelberg.https://doi.org/10.1007/3-540-36970-8_9 

Dellnitz, M., Schÿfdtze, O., &; Hestermeyer, T. (2005). Covering Pareto Sets by Multilevel Subdivision Techniques. Journal of Optimization Theory and Applications, 113–136.https://doi.org/10.1007/s10957-004-6468-7 

Dellnitz, M., Field, M., Golubitsky, M., Ma, J., &; Hohmann, A. (1995). Cycling Chaos. International Journal of Bifurcation and Chaos, 1243–1247.https://doi.org/10.1142/s0218127495000909 

Klus, S., Nüske, F., Peitz, S., Niemann, J.-H., Clementi, C., &; Schütte, C. (2020). Data-driven approximation of the Koopman generator: Model reduction, system identification, and control. Physica D: Nonlinear Phenomena, 406.https://doi.org/10.1016/j.physd.2020.132416 

Peitz, S., Otto, S. E., &; Rowley, C. W. (2020). Data-Driven Model Predictive Control using Interpolated Koopman  Generators. SIAM Journal on Applied Dynamical Systems, 19(3), 2162–2193.https://doi.org/10.1137/20M1325678 

Klus, S., Nüske, F., Koltai, P., Wu, H., Kevrekidis, I., Schütte, C., &; Noé, F. (2018). Data-Driven Model Reduction and Transfer Operator Approximation. Journal of Nonlinear Science, 985–1010.https://doi.org/10.1007/s00332-017-9437-7 

Bieker, K., Peitz, S., Brunton, S. L., Kutz, J. N., &; Dellnitz, M. (2020). Deep model predictive flow control with limited sensor data and online learning. Theoretical and Computational Fluid Dynamics, 34, 577–591.https://doi.org/10.1007/s00162-020-00520-4 

Berkemeier, M. B., &; Peitz, S. (2021). Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models. Mathematical and Computational Applications, 26(2).https://doi.org/10.3390/mca26020031 

Li, R., Pottharst, A., Frohieke, N., Becker, J., Witting, K., Dellnitz, M.,https://doi.org/10.1109/apec.2005.1452979__Feldmann, R. (2005). Design and implementation of a hybrid energy supply system for railway vehicles. In Twentieth Annual IEEE Applied Power Electronics Conference and Exposition, 2005. APEC 2005.https://doi.org/10.1109/apec.2005.1452979 

Schütze, O., Vasile, M., Junge, O., Dellnitz, M., &; Izzo, D. (2009). Designing optimal low-thrust gravity-assist trajectories using space pruning and a multi-objective approach. Engineering Optimization, 155–181.https://doi.org/10.1080/03052150802391734 

Froyland, G., &; Dellnitz, M. (2003). Detecting and Locating Near-Optimal Almost-Invariant Sets and Cycles. SIAM Journal on Scientific Computing, 1839–1863.https://doi.org/10.1137/s106482750238911x 

Thiere, B., Ober-Blöbaum, S., &; Pergola, P. (2010). Detecting Initial Guesses for Trajectories in the (P)CRTBP. In AIAA/AAS Astrodynamics Specialist Conference.https://doi.org/10.2514/6.2010-7962 

Barany, E., Dellnitz, M., &; Golubitsky, M. (1993). Detecting the symmetry of attractors. Physica D: Nonlinear Phenomena, 66–87.https://doi.org/10.1016/0167-2789(93)90198-a 

Froyland, G., Padberg, K., England, M. H., &; Treguier, A. M. (2007). Detection of Coherent Oceanic Structures via Transfer Operators. Physical Review Letters.https://doi.org/10.1103/physrevlett.98.224503 

Elsässer, R., Monien, B., &; Preis, R. (2002). Diffusion Schemes for Load Balancing on Heterogeneous Networks. Theory of Computing Systems, 305–320.https://doi.org/10.1007/s00224-002-1056-4 

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Leyendecker, S., Ober-Blöbaum, S., Marsden, J. E., &; Ortiz, M. (2007). Discrete Mechanics and Optimal Control for Constrained Multibody Dynamics. In Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C.https://doi.org/10.1115/detc2007-34574 

Demoures, F., Gay-Balmaz, F., Leyendecker, S., Ober-Blöbaum, S., Ratiu, T. S., &; Weinand, Y. (2015). Discrete variational Lie group formulation of geometrically exact beam dynamics. Numerische Mathematik, 73–123.https://doi.org/10.1007/s00211-014-0659-4 

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Dellnitz, M., Hüllermeier, E., Lücke, M., Ober-Blöbaum, S., Offen, C., Peitz, S., &; Pfannschmidt, K. (2023). Efficient time stepping for numerical integration using reinforcement  learning. SIAM Journal on Scientific Computing, 45(2), 9–5.https://doi.org/10.1137/21M1412682 

Peitz, S., Dellnitz, M., &; Bannenberg, S. (2022). Efficient Virtual Design and Testing of Autonomous Vehicles. In H. G. Bock, K.-H. Küfer, P. Maas, A. Milde, &; V. Schulz (Eds.), German Success Stories in Industrial Mathematics (Vol. 35). Springer International Publishing.https://doi.org/10.1007/978-3-030-81455-7_23 

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Flaskamp, K., &; Ober-Blobaum, S. (2012). Energy efficient control for mechanical systems based on inherent dynamical structures. In 2012 American Control Conference (ACC).https://doi.org/10.1109/acc.2012.6314820 

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Hernández Castellanos, C. I., Ober-Blöbaum, S., &; Peitz, S. (2020). Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty. International Journal of Robust and Nonlinear Control, 30(17), 7593–7618.https://doi.org/10.1002/rnc.5197 

Ober-Blöbaum, S., &; Peitz, S. (2021). Explicit multiobjective model predictive control for nonlinear systems  with symmetries. International Journal of Robust and Nonlinear Control, 31(2), 380–403.https://doi.org/10.1002/rnc.5281 

Dellnitz, M., Hohmann, A., Junge, O., &; Rumpf, M. (1997). Exploring invariant sets and invariant measures. Chaos: An Interdisciplinary Journal of Nonlinear Science, 221–228.https://doi.org/10.1063/1.166223 

Froyland, G. (2001). Extracting Dynamical Behavior via Markov Models. In Nonlinear Dynamics and Statistics. Boston, MA.https://doi.org/10.1007/978-1-4612-0177-9_12 

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Sonntag, K., &; Peitz, S. (2024). Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems. Journal of Optimization Theory and Applications.https://doi.org/10.1007/s10957-024-02389-3 

Peitz, S., &; Klus, S. (2020). Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models Based on the Koopman Operator. In Lecture Notes in Control and Information Sciences (Vol. 484, pp. 257–282). Cham: Springer.https://doi.org/10.1007/978-3-030-35713-9_10 

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Hanke, S., Peitz, S., Wallscheid, O., Böcker, J., &; Dellnitz, M. (2019). Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification. In 2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE).https://doi.org/10.1109/precede.2019.8753313 

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Dellnitz, M., Melbourne, I., &; Marsden, J. E. (1992). Generic bifurcation of Hamiltonian vector fields with symmetry. Nonlinearity, 979–996.https://doi.org/10.1088/0951-7715/5/4/008 

Dellnitz, M., Marsden, J. E., Melbourne, I., &; Scheurle, J. (1992). Generic Bifurcations of Pendula. In Bifurcation and Symmetry. Basel.https://doi.org/10.1007/978-3-0348-7536-3_10 

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Grüne, L., &; Junge, O. (2007). Global Optimal Control of Perturbed Systems. Journal of Optimization Theory and Applications, 411–429.https://doi.org/10.1007/s10957-007-9312-z 

Chaudhuri, I., Sertl, S., Hajnal, Z., Dellnitz, M., &; Frauenheim, T. (2004). Global optimization of silicon nanoclusters. Applied Surface Science, 108–113.https://doi.org/10.1016/j.apsusc.2003.11.007 

Sertl, S., &; Dellnitz, M. (2006). Global Optimization using a Dynamical Systems Approach. Journal of Global Optimization, 569–587.https://doi.org/10.1007/s10898-005-4384-5 

Peitz, S., &; Dellnitz, M. (2017). Gradient-Based Multiobjective Optimization with Uncertainties. In NEO 2016 (pp. 159–182). Cham.https://doi.org/10.1007/978-3-319-64063-1_7 

Dellnitz, M., Molo, M. H., Metzner, P., Preis, R., &; Schütte, C. (2006). Graph Algorithms for Dynamical Systems. In Analysis, Modeling and Simulation of Multiscale Problems.https://doi.org/10.1007/3-540-35657-6_23 

Ringkamp, M., Ober-Blöbaum, S., Dellnitz, M., &; Schütze, O. (2012). Handling high-dimensional problems with multi-objective continuation methods via successive approximation of the tangent space. Engineering Optimization, 1117–1146.https://doi.org/10.1080/0305215x.2011.634407 

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Campos, C. M., Ober-Blöbaum, S., &; Trélat, E. (2015). High order variational integrators in the optimal control of mechanical systems. Discrete &; Continuous Dynamical Systems - A, 35(9), 4193–4223.https://doi.org/10.3934/dcds.2015.35.4193 

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Schütze, O., Coello Coello, C. A., Mostaghim, S., Talbi, E.-G., &; Dellnitz, M. (2008). Hybridizing evolutionary strategies with continuation methods for solving multi-objective problems. Engineering Optimization, 383–402.https://doi.org/10.1080/03052150701821328 

von der Gracht, S., Nijholt, E., &; Rink, B. (2023). Hypernetworks: Cluster Synchronization Is a Higher-Order Effect. SIAM Journal on Applied Mathematics, 83(6), 2329–2353.https://doi.org/10.1137/23m1561075 

Gölz, C., Voelcker-Rehage, C., Mora, K., Reuter, E.-M., Godde, B., Dellnitz, M.,https://doi.org/10.3389/fphys.2018.01540__Vieluf, S. (2018). Improved Neural Control of Movements Manifests in Expertise-Related Differences in Force Output and Brain Network Dynamics. Frontiers in Physiology.https://doi.org/10.3389/fphys.2018.01540 

Zanzottera, A., Mingotti, G., Castelli, R., &; Dellnitz, M. (2012). Intersecting invariant manifolds in spatial restricted three-body problems: Design and optimization of Earth-to-halo transfers in the Sun–Earth–Moon scenario. Communications in Nonlinear Science and Numerical Simulation, 832–843.https://doi.org/10.1016/j.cnsns.2011.06.032 

Gebken, B., &; Peitz, S. (2021). Inverse multiobjective optimization: Inferring decision criteria from data. Journal of Global Optimization, 80, 3–29.https://doi.org/10.1007/s10898-020-00983-z 

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