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STAFF   Jeroen Lamb     Martin Rasmussen     Dmitry Turaev     Sebastian van Strien   HONORARY STAFF Tiago Pereira POSTDOCS Dongchen Li Iacopo Longo Eeltje Nijholt Doan Thai Son PHD STUDENTS Bernat Bassols-Cornudella Chris Chalhoub Hugo Chu Matheus de Castro Akshunna Dogra Michal Fedorowicz David Fox Emilia Gibson Vincent Goverse Amir Khodaeian Karim Victoria Klein Chek Lau Ziyu Li Tianyi Liu Dmitrii Mints Leon Staresinic Giuseppe Tenaglia VISITORS Ole Peters Cristina Sargent Bill Speares RELATED STAFF Mauricio Barahona Davoud Cheraghi Martin Hairer Darryl Holm Xue-Mei Li Greg Pavliotis Kevin Webster

PROFESSOR MARTIN RASMUSSEN Professor of Mathematics Phone: +44(207)59-42774 Room: 637 Huxley Building PHD STUDENTS Chris Chalhoub Hugo Chu Matheus de Castro Michal Fedorowicz David Fox Ziyu Li POSTDOCS Iacopo Longo Doan Thai Son

Areas of interest My research aims at the development of the Qualitative Theory of Nonautonomous and Random Dynamical Systems. In particular, I have made contributions to the following areas: stability and attractor theory, bifurcation theory, theory of invariant manifolds, and Morse decomposition theory. My Google Scholar page My Mathematics Genealogy page Grants, Awards and Prizes Marie Sklodowska-Curie Fellowship (Researcher: Doan Thai Son), 2022–2025. Imperial College London, Faculty of Natural Sciences Prize for Excellence in Personal Tutoring & Pastoral Support, 2019. Marie Sklodowska-Curie Fellowship (Researcher: Gabriel Fuhrmann), 2018–2020. Marie Sklodowska-Curie Innovative Training Network on Critical Transitions in Complex Systems (co-PI with Jeroen Lamb), 2015–2019. Marie Curie IEF Fellowship (Researcher: Janosch Rieger), 2015–2017. EPSRC Grant New Directions for Research Leaders, 2013–2015. Marie Curie IEF Fellowship (Researcher: Vasso Anagnostopoulou), 2013–2016. Marie Curie IEF Fellowship (Researcher: Doan Thai Son, co-PI with Jeroen Lamb), 2013–2015. EPSRC Career Acceleration Fellowship, 2010–2015. Marie Curie IEF Fellowship (Researcher), 2008–2010. Postdoctoral Grant from the State of Bavaria, 2006–2007, University of Augsburg. The article Towards a Bifurcation Theory for Nonautonomous Difference Equations was awarded the prize of the best paper in 2006 by the International Society of Difference Equations (ISDE). Grant for excellent undergraduate studies from the Department of Mathematics at the University of Augsburg, 1999–2000. Publications Books: Vasso Anagnostopoulou, Christian Pötzsche, and Martin Rasmussen, Nonautonomous Bifurcation Theory – Concepts and Tools, Frontiers in Applied Dynamical Systems: Reviews and Tutorials 10, Springer, Cham, 2023. Article MathSciNet Peter E. Kloeden and Martin Rasmussen, Nonautonomous dynamical systems, Mathematical Surveys and Monographs 176, American Mathematical Society, Providence, 2011. MathSciNet Martin Rasmussen, Attractivity and bifurcation for nonautonomous dynamical systems, Lecture Notes in Mathematics 1907, Springer, Berlin, 2007. MathSciNet Submitted journal articles: Jeroen S. W. Lamb, Martin Rasmussen, and Wei Hao Tey, Attractors of Linear Maps with Bounded Noise. DynamIC Preprint 2023-2 Konstantinos Kourliouros, Jeroen S. W. Lamb, Martin Rasmussen, Wei Hao Tey, Kalle G. Timperi, and Dmitry Turaev, Persistence of minimal invariant sets for certain set-valued dynamical systems: a boundary mapping approach. DynamIC Preprint 2023-1 Lea Oljaca, Peter Ashwin, and Martin Rasmussen, Measure and statistical attractors for nonautonomous dynamical systems. DynamIC Preprint 2022-3 Matheus M. Castro, Vincent P. H. Goverse, Jeroen S. W. Lamb, and Martin Rasmussen, On the quasi-ergodicity of absorbing Markov chains with unbounded transition densities, including random logistic maps with escape. DynamIC Preprint 2022-2 Matheus M. Castro, Dennis Chemnitz, Hugo Chu, Maximilian Engel, Jeroen S. W. Lamb, and Martin Rasmussen, The Lyapunov spectrum for conditioned random dynamical systems. DynamIC Preprint 2022-1 Matheus M. Castro, Jeroen S. W. Lamb, Guillermo Olicón Méndez, and Martin Rasmussen, Existence and uniqueness of quasi-stationary and quasi-ergodic measures for absorbing Markov chains: a Banach lattice approach . DynamIC Preprint 2021-3 Jeroen S. W. Lamb, Martin Rasmussen, and Kalle Timperi, On boundaries of epsilon-neighbourhoods of planar sets, Part II: global structure and curvature. DynamIC Preprint 2021-2 Jeroen S. W. Lamb, Martin Rasmussen, and Kalle Timperi, On boundaries of epsilon-neighbourhoods of planar sets, Part I: Singularities. DynamIC Preprint 2020-7 Mickael D. Chekroun, Jeroen S.W. Lamb, Christian J. Pangerl, and Martin Rasmussen, A Girsanov approach to slow parameterizing manifolds in the presence of noise. DynamIC Preprint 2019-7 Thai Son Doan, Jeroen S.W. Lamb, Julian Newman, and Martin Rasmussen, Classification of random circle homeomorphisms up to topological conjugacy. DynamIC Preprint 2018-3 Journal articles: George Chappelle, Alan Hastings, and Martin Rasmussen, Pool dynamics of time-dependent compartmental systems with application to the terrestrial carbon cycle, Journal of the Royal Society Interface 20(2023), 20220843. Article George Chappelle, Alan Hastings, and Martin Rasmussen, Occupancy times for time-dependent stage-structured models, Journal of Mathematical Biology 84, 3 (2022), Paper No. 16, 17. Article MathSciNet Preprint Fritz Colonius and Martin Rasmussen, Quasi-ergodic limits for finite absorbing Markov chains, Linear Algebra and its Applications 609(2021), 253−288. Article MathSciNet Preprint Iacopo P. Longo, Carmen Núñez, Rafael Obaya, and Martin Rasmussen, Rate-induced tipping and saddle-node bifurcation for quadratic differential equations with nonautonomous asymptotic dynamics, SIAM Journal on Applied Dynamical Systems 20, 1 (2021), 500−540. Article MathSciNet Preprint Moussa Ndour, Kathrin Padberg-Gehle, and Martin Rasmussen, Spectral early-warning signals for sudden changes in time-dependent flow patterns., Fluids 6(2021), 49. Article Peter Giesl, Boumediene Hamzi, Martin Rasmussen, and Kevin Webster, Approximation of Lyapunov functions from noisy data, Journal of Computational Dynamics 7, 1 (2020), 57−81. Article MathSciNet Preprint Maximilian Engel, Jeroen S. W. Lamb, and Martin Rasmussen, Conditioned Lyapunov exponents for random dynamical systems, Transactions of the American Mathematical Society 372, 9 (2019), 6343−6370. Article MathSciNet Preprint Maximilian Engel, Jeroen S. W. Lamb, and Martin Rasmussen, Bifurcation analysis of a stochastically driven limit cycle, Communications in Mathematical Physics 365, 3 (2019), 935−942. Article MathSciNet Preprint Thai Son Doan, Maximilian Engel, Jeroen S. W. Lamb, and Martin Rasmussen, Hopf bifurcation with additive noise, Nonlinearity 31, 10 (2018), 4567−4601. Article MathSciNet Preprint Christian Kuehn, Giuseppe Malavolta, and Martin Rasmussen, Early-warning signals for bifurcations in random dynamical systems with bounded noise, Journal of Mathematical Analysis and Applications 464, 1 (2018), 58−77. Article MathSciNet Preprint Martin Rasmussen, Janosch Rieger, and Kevin Webster, A reinterpretation of set differential equations as differential equations in a Banach space, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 148, 2 (2018), 429−446. Article MathSciNet Preprint Mark Callaway, Thai Son Doan, Jeroen S. W. Lamb, and Martin Rasmussen, The dichotomy spectrum for random dynamical systems and pitchfork bifurcations with additive noise, Annales de l'Institut Henri Poincaré Probabilités et Statistiques 53, 4 (2017), 1548−1574. Article MathSciNet Preprint Anna Maria Cherubini, Jeroen S. W. Lamb, Martin Rasmussen, and Yuzuru Sato, A random dynamical systems perspective on stochastic resonance, Nonlinearity 30, 7 (2017), 2835−2853. Article MathSciNet Preprint Thai Son Doan, Kenneth J. Palmer, and Martin Rasmussen, The Bohl spectrum for linear nonautonomous differential equations, Journal of Dynamics and Differential Equations 29, 4 (2017), 1459−1485. Article MathSciNet Preprint Yiqi Luo, Zheng Shi, Xingjie Lu, Jianyang Xia, Junyi Liang, Jiang Jiang, Ying Wang, Matthew J. Smith, Lifen Jiang, Anders Ahlström, Benito Chen, Oleksandra Hararuk, Alan Hastings, Forrest Hoffman, Belinda Medlyn, Shuli Niu, Martin Rasmussen, Katherine Todd-Brown, and Ying-Ping Wang, Transient dynamics of terrestrial carbon storage: mathematical foundation and its applications, Biogeosciences 14(2017), 145−161. Article Martin Rasmussen, Janosch Rieger, and Kevin N. Webster, Approximation of reachable sets using optimal control and support vector machines, Journal of Computational and Applied Mathematics 311(2017), 68−83. Article MathSciNet Preprint Martin Rasmussen, Alan Hastings, Matthew J. Smith, Folashade B. Agusto, Benito M. Chen-Charpentier, Forrest M. Hoffman, Jiang Jiang, Katherine E. O. Todd-Brown, Ying Wang, Ying-Ping Wang, and Yiqi Luo, Transit times and mean ages for nonautonomous and autonomous compartmental systems, Journal of Mathematical Biology 73, 6−7 (2016), 1379−1398. Article MathSciNet Preprint Ying-Ping Wang, Jiang Jiang, Benito Chen-Charpentier, Folashade B. Agusto, Alan Hastings, Forrest Hoffman, Martin Rasmussen, Matthew J. Smith, Katherine Todd-Brown, Ying Wang, Xia Xu, and Yiqi Luo, Responses of two nonlinear microbial models to warming and increased carbon input, Biogeosciences 13(2016), 887−902. Article Thai Son Doan, Martin Rasmussen, and Peter E. Kloeden, The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor, Discrete and Continuous Dynamical Systems B 20, 3 (2015), 875−887. Article MathSciNet Preprint Jeroen S. W. Lamb, Martin Rasmussen, and Christian S. Rodrigues, Topological bifurcations of minimal invariant sets for set-valued dynamical systems, Proceedings of the American Mathematical Society 143, 9 (2015), 3927−3937. Article MathSciNet Preprint Tiago Pereira, Jaap Eldering, Martin Rasmussen, and Alexei Veneziani, Towards a theory for diffusive coupling functions allowing persistent synchronization, Nonlinearity 27, 3 (2014), 501−525. Article MathSciNet Preprint Ying-Ping Wang, Benito Chen, William R. Wieder, Yiqi Luo, Maria Leite, Belinda E. Medlyn, Martin Rasmussen, Matthew J. Smith, Folashade B. Agusto, and Forrest Hoffman, Oscillatory behavior of two nonlinear microbial models of soil carbon decomposition, Biogeosciences  11, 7 (2014), 1817−1831. Article Peter Giesl and Martin Rasmussen, Areas of attraction for nonautonomous differential equations on finite time intervals, Journal of Mathematical Analysis and Applications 390, 1 (2012), 27−46. Article MathSciNet Peter E. Kloeden, Christian Pötzsche, and Martin Rasmussen, Limitations of pullback attractors for processes, Journal of Difference Equations and Applications 18, 4 (2012), 693−701. Article MathSciNet Peter Giesl and Martin Rasmussen, A note on almost periodic variational equations, Communications on Pure and Applied Analysis 10, 3 (2011), 983−994. Article MathSciNet Fritz Colonius, Thorsten Hüls, and Martin Rasmussen, Connecting orbits in perturbed systems, Nonlinear Dynamics 59, 4 (2010), 569−578. Article MathSciNet Christian Pötzsche and Martin Rasmussen, Computation of integral manifolds for Carathéodory differential equations, IMA Journal of Numerical Analysis 30, 2 (2010), 401−430. Article MathSciNet Martin Rasmussen, An alternative approach to Sacker-Sell spectral theory, Journal of Difference Equations and Applications 16, 2−3 (2010), 227−242. Article MathSciNet Martin Rasmussen, Finite-time attractivity and bifurcation for nonautonomous differential equations, Differential Equations and Dynamical Systems 18, 1−2 (2010), 57−78. Article MathSciNet Christian Pötzsche and Martin Rasmussen, Computation of nonautonomous invariant and inertial manifolds, Numerische Mathematik 112, 3 (2009), 449−483. Article MathSciNet Martin Rasmussen, Dichotomy spectra and Morse decompositions of linear nonautonomous differential equations, Journal of Differential Equations 246, 6 (2009), 2242−2263. Article MathSciNet Fritz Colonius, Peter E. Kloeden, and Martin Rasmussen, Morse spectrum for nonautonomous differential equations, Stochastics and Dynamics 8, 3 (2008), 351−363. Article MathSciNet Peter Giesl and Martin Rasmussen, Borg's criterion for almost periodic differential equations, Nonlinear Analysis. Theory, Methods & Applications 69, 11 (2008), 3722−3733. Article MathSciNet Martin Rasmussen, All-time Morse decompositions of linear nonautonomous dynamical systems, Proceedings of the American Mathematical Society 136, 3 (2008), 1045−1055. Article MathSciNet Martin Rasmussen, Bifurcations of asymptotically autonomous differential equations, Set-Valued Analysis 16, 7−8 (2008), 821−849. Article MathSciNet Martin Rasmussen, Nonautonomous bifurcation patterns for one-dimensional differential equations, Journal of Differential Equations 234, 1 (2007), 267−288. Article MathSciNet Martin Rasmussen, Morse decompositions of nonautonomous dynamical systems, Transactions of the American Mathematical Society 359, 10 (2007), 5091−5115. Article MathSciNet Bernd Aulbach, Martin Rasmussen, and Stefan Siegmund, Invariant manifolds as pullback attractors of nonautonomous differential equations, Discrete and Continuous Dynamical Systems A 15, 2 (2006), 579−596. Article MathSciNet Christian Pötzsche and Martin Rasmussen, Taylor approximation of integral manifolds, Journal of Dynamics and Differential Equations 18, 2 (2006), 427−460. Article MathSciNet Martin Rasmussen, Towards a bifurcation theory for nonautonomous difference equations, Journal of Difference Equations and Applications 12, 3−4 (2006), 297−312. Article MathSciNet Bernd Aulbach, Martin Rasmussen, and Stefan Siegmund, Approximation of attractors of nonautonomous dynamical systems, Discrete and Continuous Dynamical Systems B 5, 2 (2005), 215−238. Article MathSciNet Christian Pötzsche and Martin Rasmussen, Taylor approximation of invariant fiber bundles for nonautonomous difference equations, Nonlinear Analysis. Theory, Methods & Applications 60, 7 (2005), 1303−1330. Article MathSciNet Articles in conference proceedings: Peter E. Kloeden, Christian Pötzsche, and Martin Rasmussen, Discrete-time nonautonomous dynamical systems, in: Stability and bifurcation theory for non-autonomous differential equations, Lecture Notes in Mathematics, 35−102, Springer, Heidelberg, 2013. Article MathSciNet Christian Pötzsche and Martin Rasmussen, Hibernation prevents chaos: a logistic case study, in: Difference equations and applications (M. Bohner, Z. Doslá, G. Ladas, M. Ünal, A. Zafer), 259−274, Uğur-Bahçeşehir Univ. Publ. Co., Istanbul, 2009. MathSciNet Bernd Aulbach, Martin Rasmussen, and Stefan Siegmund, Invariant manifolds as pullback attractors of nonautonomous difference equations, in: Proceedings of the Eighth International Conference on Difference Equations and Applications (S. Elaydi, G. Ladas, B. Aulbach, O. Dosly), 23−37, CRC, Boca Raton, 2005. Article MathSciNet Christian Pötzsche and Martin Rasmussen, Local approximation of invariant fiber bundles: an algorithmic approach, in: Difference equations and discrete dynamical systems (L. Allen, B. Aulbach, S. Elaydi, R. Sacker), 155−170, World Scientific, Singapore, 2005. Article MathSciNet Miscellaneous: Attractivity and Bifurcation for Nonautonomous Dynamical Systems, PhD Thesis, University of Augsburg, 2006, 190 pages. Approximation von Attraktoren und Mannigfaltigkeiten nichtautonomer Systeme, Diploma Thesis, University of Augsburg, 2002, 119 pages. Download Bevölkerungsprognose für Augsburg 2000–2015 (with H. Glöckner), Beiträge zur Stadtentwicklung, Stadtforschung und Statistik 18, Stadt Augsburg, 2000, 386 pages.