Personal profile
Stephen Wiggins is renowned for his pioneering research in applied mathematics, with emphasis on nonlinear dynamics, chaos theory, and geometry and transport in phase space. His work has advanced the understanding of phase space structures, mixing, and transport in dynamical systems, with applications ranging from fluid mechanics to chemical reaction dynamics. Wiggins’s research themes connect mathematical foundations with practical scientific challenges, synergistically influencing fields such as theoretical chemistry and geophysical transport.
Research Interests
Lagrangian Transport
Investigating transport and mixing in geophysical flows (oceanic and atmospheric) using dynamical systems theory, focusing on hyperbolic trajectories and invariant manifolds.
Chemical Reaction Dynamics
Exploring phase space structures in reaction dynamics, including "roaming" mechanisms, transition state theory, and phase space conduits for energy transfer.
Lagrangian Descriptors
Developing and applying the method of Lagrangian descriptors—a trajectory-based scalar field technique—to reveal phase space structures in complex, aperiodically time-dependent systems.
Educational Background
B.S. in Physics and Mathematics, Pittsburg State University, 1977
M.S. in Mathematics, University of Wisconsin-Madison, 1980
M.S. in Physics, University of Wisconsin-Madison, 1980
Ph.D. in Theoretical and Applied Mechanics, Cornell University, 1983
Work Experience
2001-2026 University of Bristol, Bristol, UK
Professor of Applied Mathematics
2022- United States Naval Academy, Annapolis, MD, USA
William R. Davis ’68 Distinguished Chair in Mathematics
Honours and Awards
NSF Presidential Young Investigator Award, 1989.
Stanislaw M. Ulam Visiting Scholar at the Center for Nonlinear Studies, Los Alamos National
Laboratory, 1989-1990.
ONR Young Investigator Award in Applied Analysis, 1989.
Visiting Scientist at the Fields Institute for Research in Mathematical Sciences, Waterloo, Canada,
January 1 - March 31, 1993. Presented a course on my research in nonlinear dynamics.
1998-99 Caltech Graduate Student Council Teaching Award.
Books
[1] Wiggins, S. (1988). Global bifurcations and chaos: Analytical methods. Springer. https://doi.org/10.1007/978-1-4612-1042-9
[2] Wiggins, S. (1992). Chaotic transport in dynamical systems. Springer. https://doi.org/10.1007/978-1-4757-3896-4
[3] Wiggins, S. (1993). Global dynamics, phase space transport, orbits homoclinic to resonances, and applications. American Mathematical Society.
[4] Wiggins, S. (1994). Normally hyperbolic invariant manifolds in dynamical systems. Springer. https://doi.org/10.1007/978-1-4612-4312-0
[5] Li, Y., & Wiggins, S. (1997). Invariant manifolds and fibrations for perturbed nonlinear Schrödinger equations.
Springer. https://doi.org/10.1007/978-1-4612-1838-8
[6] Wiggins, S. (2003). Introduction to applied nonlinear dynamical systems and chaos (2nd ed.).
Springer. https://doi.org/10.1007/b97481
[7] Samelson, R. M., & Wiggins, S. (2006). Lagrangian transport in geophysical jets and waves: The dynamical systems approach.
Springer. https://doi.org/10.1007/978-0-387-46213-4
[8] Sturman, R., Ottino, J. M., & Wiggins, S. (2006). The mathematical foundations of mixing: The linked twist map as a paradigm in
applications: Micro to macro, fluids to solids. Cambridge University Press. https://doi.org/10.1017/CBO9780511618116
[9] Wiggins, S. (2017). Elementary classical mechanics. World Scientific. https://doi.org/10.1142/13443
[10] Wiggins, S. (2017). Ordinary differential equations: A dynamical point of view. World Scientific. https://doi.org/10.1142/13548
[11] Wiggins, S. (2018). Elementary classical mechanics: Problems and solutions. World Scientific. https://doi.org/10.1142/13444
[12] Wiggins, S. (2020). Elementary quantum mechanics: With problems and solutions. World Scientific. https://doi.org/10.1142/14071
[13] Wiggins, S., GarcíaGarrido, V. J., Katsanikas, M., & Ratanpara, A. (2024). Phase space structures in reaction
dynamics: A dynamical systems approach. World Scientific. https://doi.org/10.1142/14372
Publications
Mauguière, F. A. L., Collins, P., Kramer, Z. C., Carpenter, B. K., Ezra, G. S., Farantos, S. C., & Wiggins, S. (2017). Roaming: A phase space perspective. Annual Review of Physical Chemistry, 68, 499-524. https://doi.org/10.1146/annurev-physchem-052516-050613
Wiggins, S. (2005). The dynamical systems approach to Lagrangian transport in oceanic flows. Annual Review of Fluid Mechanics, 37, 295-328. https://doi.org/10.1146/annurev.fluid.37.061903.175815
Wiggins, S., & García-Garrido, V. J. (2022). Painting the phase portrait of a dynamical system with Lagrangian descriptors. Notices of the American Mathematical Society, 69(6), 936-948.https://doi.org/10.1090/noti2489
Chen, N., Wiggins, S., & Andreou, M. (2025). Taming uncertainty in a complex world: The rise of uncertainty quantification – a tutorial for beginners. Notices of the American Mathematical Society, 72(3), 250-260. https://doi.org/10.1090/noti3120