Research Group
Members
Postdocs
From 02/2024: Zachary Adams, FU Berlin: "A new approach to metastability in multi-agent systems"
From 09/2022: Tobias Hurth, FU Berlin: "An ergodic theory for conditioned random dynamical systems"
10/2021 - 09/2023: G. Olicon-Mendez, FU Berlin: "Random bifurcations in chemical reaction networks"
PhD students
Since 04/2022: R. Chemnitz, FU Berlin: "Characterization of quasi-stationary states"
Since 03/2022: M. Eser, FU Berlin: "Inter-layer synchronization in networks with time-varying topology"
Since 11/2021: D. Chemnitz, FU Berlin: "Random dynamics of stochastic gradient descent"
Master students
05-07/2023: Maxime Eidelsberg, ESPCI PARIS - PSL: "Machine learning methods for covariant Lyapunov vectors"
Visitors
22/05 - 14/07/2023: Alex Blumenthal (Georgia Tech) as MATH+ Visiting Scholar
01/05 - 21/07/2023: Maxime Eidelsberg (ESPCI PARIS - PSL) as research intern
06/02 - 07/02/2023: Ludwig Arnold (Bremen) and Peter Kloeden (Tübingen)
24/01 - 27/01/2023: Xue-Mei Li (Imperial College London and EPFL Lausanne)
04/07 - 07/07/2022: Maxime Breden (Ecole Polytechnique)
20/06 - 24/06/2022: Hildeberto Jardon-Kojakhmetov (University of Groningen)
22/05-25/05/2022: Iacopo Longo (TU Munich)
02 - 07/2022: Mustafa Riza (Eastern Mediterrenean University)
Publications
2024
R. Chemnitz, M. Engel and G. Olicon-Mendez, Random attractors on countable state spaces, 2024, arXiv, pp. 1-44.
L. G. Venegas-Pineda, H. Jardon-Kojakhmetov, M. Engel, J. Heitzig, M. C. Eser, M. Cao, Strategic control for a Boltzmann like decision-making model, 2024, arXiv, pp. 1-40.
R. Chemnitz, M. Engel and P. Koltai, Extracting coherent sets in aperiodically driven flows from generators of Mather semigroups, 2024, arXiv, pp. 1-51.
M. Engel, P. Friz and T. Orenshtein, Nonlinear effects within invariance principles, 2024, arXiv, pp. 1-22.
Z.P. Adams: Quasi-ergodicity of transient patterns in stochastic reaction-diffusion equations, Electr. J. Probab. 29: 2024, 1-29, DOI
M. Engel, G. Olicon-Mendez, N. Unger, S. Winkelmann, Synchronization and random attractors for reaction jump processes, Journal of Dynamics and Differential Equations, 2024 , DOI, pp. 1-36.
R. Chemnitz, M. Engel and P. Koltai. Continuous-time extensions of discrete-time cocycles, Proceedings of the AMS ,11: 23-35, 2024, DOI.
M.M. Castro, D. Chemnitz, H. Chu, M. Engel, J.S.W. Lamb, M. Rasmussen, The Lyapunov spectrum for conditioned random dynamical systems, 2024, to appear in Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, arXiv version, pp. 1-36.
2023
A. Blumenthal, M. Engel and A. Neamtu, On the pitchfork bifurcation for the Chafee-Infante equation with additive noise, Probability Theory and Related Fields, 187: 603-627, 2023, DOI.
T. Hurth, K. Khanin, B. Navarro Lameda, F. Nazarov. On a Factorization Formula for the Partition Function of Directed Polymers. J Stat Phys ,190, 165, 2023, DOI
M. Engel, G. Piliouras, A stochastic variant of replicator dynamics in zero-sum games and its invariant measures, 2023, Physica D: Nonlinear Phenomena, 456: 133940, 2023, DOI.
M. Engel and G. Olicon-Mendez, Noise-induced instabilities in a stochastic Brusselator, 2023, arXiv, pp. 1-17, to appear in Contemporary Mathematics.
M. Breden and M. Engel, Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems, Annals of Applied Probability, 33(2): 1052-1094, 2023, DOI.
D. Chemnitz, M. Engel, Positive Lyapunov Exponent in the Hopf Normal Form with Additive Noise, Communications in Mathematical Physics: 402: 1807–1843, 2023, DOI.
M. Engel, G. Gottwald, Canards in modified equations for Euler discretizations, 2023, arXiv, pp.1-13, to appear in Contemporary Mathematics.
R. Chemnitz, Sensitivity of steady states in networks with application to Markov chains and chemical reaction networks, 2023, SIAM Journal of Applied Mathematics, 83(4): 1444-1466, DOI.
2022
M. Benaim and T. Hurth, Markov chains on metric spaces. A short course. Universitext, Springer, 2022, DOI
A. Viennet, N. Vercauteren, M. Engel and D. Faranda, Guidelines for data-driven approaches to study transitions in multiscale systems: the case of Lyapunov vectors, Chaos 32:11, 2022, DOI.
M. Engel, C. Kuehn and B. de Rijk, A traveling wave bifurcation analysis of turbulent pipe flow, Nonlinearity 35:11, 2022, DOI.
M. Engel, C.Kuehn, M.Petrera and Y. Suris, Discretized fast-slow systems with canards in two dimensions, Journal of Nonlinear Science 32:19, 2022, DOI .
C.Kuehn, N. Berglund, C. Bick, M. Engel, T. Hurth, A. Iuorio, and C. Soresina, A general view on double limits in differential equations, Physica D: Nonlinear Phenomena 431, 2022, DOI.
M. Engel, F. Hummel, C. Kuehn, N. Popovic, M. Ptashnyk, T. Zacharis, Geometric analysis of fast-slow PDEs with fold singularities, 2022, arXiv version, preprint under review.
2021
M. Engel, F. Hummel and C. Kuehn, Connecting a direct and a Galerkin approach to slow manifolds in infinite dimensions, Proceedings of the AMS, Series B 8, 2021, DOI.
M.Engel, M. Gkogkas and C. Kuehn, Homogenization of Fully-Coupled Chaotic Fast-Slow Systems via Intermediate Stochastic Regularization, Journal of Statistical Physics 183, 2021, DOI.
M.Engel and C.Kuehn, A random dynamical systems perspective on isochronicity for stochastic oscillations, Communications in Mathematical Physics 386(3), 2021, DOI,
M.M. Castro, J.S.W. Lamb, G. Olicon-Mendez, M. Rasmussen, Existence and uniqueness of quasi-stationary and quasi-ergodic measures for absorbing Markov chains: a Banach lattice approach, 2021, arXiv version , preprint under review.
M. Engel and C. Kuehn, Blow-up analysis of fast-slow PDEs with loss of hyperbolicity,, 2021, arXiv version, preprint under revision.