mathematics

Stephen Wiggins

Stephen Wiggins is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Stephen Wiggins rather than just read about it. In short: Stephen Ray Wiggins (born 1959) is a Cherokee-American prolific applied mathematician in the fields of nonlinear dynamics, chaos theory and nonlinear phenomena. His wide range of outstanding contributions include Lagrangian aspects of fluid dynamics and reaction dynamics in theoretical chemistry.

Key takeaways

Stephen Wiggins belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Stephen Wiggins to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Stephen Wiggins from memory before moving on to harder problems.

Reference excerpt

Stephen Ray Wiggins (born 1959) is a Cherokee-American prolific applied mathematician in the fields of nonlinear dynamics, chaos theory and nonlinear phenomena. His wide range of outstanding contributions include Lagrangian aspects of fluid dynamics and reaction dynamics in theoretical chemistry. He is currently a full professor at the Hetao Institute of Mathematics and Interdisciplinary Sciences, China and honorary professor in Bristol University.

Early life and education Wiggins was born in Oklahoma City, Oklahoma in 1959, and has two younger siblings. He is enrolled as a citizen of the Cherokee Nation. He received a BSc in physics and mathematics from Pittsburg State University in 1980, an MA in mathematics and an MSc in physics from the University of Wisconsin-Madison in 1983, and a PhD in theoretical and applied mechanics from Cornell University in 1985. He also attended the Open University in Great Britain, where he earned a Bachelor of Laws, with honors, in 2005.

Academic career and field of study Wiggins was influenced heavily by his PhD advisor Philip Holmes. His dissertation was on "Slowly Varying Oscillators." From 1987 to 2001, he was a professor at Caltech. He is an emeritus professor of applied mathematics in University of Bristol, where he was the head of the mathematics department from 2004 until 2008 and was the school research director. As of August 2020 Wiggins had 12 PhD students and 60 academic descendants. In 2026, he took a faculty role in Hetao Institute of Mathematics and Interdisciplinary Sciences, initiated by Shing-Tung Yau, as a professor and retaining his emeritus role in Bristol. Wiggins has contributed in many different areas of applied mathematics, science, and engineering using applied and computational dynamics as the framework for his approach and analysis. His current focus is on developing the phase space approach to chemical reaction dynamics in the setting of the CHAMPS (Chemistry and Mathematics in Phase Space) project. Previously he has established a successful US-UK-Spain research network in building a foundational connection between applied mathematics and theoretical chemistry with Turgay Uzer.

Honors Wiggins received the Presidential Young Investigators Award from the National Science Foundation (NSF) in August 1989. He was a Stanislaw M. Ulam Visiting Scholar at the Center for Nonlinear Studies, Los Alamos National Laboratory, from 1989 to 1990. He received the US Office of Naval Research (ONR) Young Investigator Award in Applied Analysis in 1989.

Selected publications Uzer, Turgay; Jaffé, C.; Palacián, J.; Yanguas Palacián, P.; Wiggins, Stephen, 2002 Nonlinearity 15 957 (Quite influential in chemical reactions). V.J.García-Garrido; M.Katsanikas; M.Agaoglou; S.Wiggins: Tuning the branching ratio in a symmetric potential energy surface with a post-transition state bifurcation using external time dependence, Chemical Physics Letters, 2020-09: DOI: 10.1016/j.cplett.2020.137714 Fang Yang; Yayun Zheng; Jinqiao Duan; Ling Fu; Stephen Wiggins: The tipping times in an Arctic sea ice system under influence of extreme events, Chaos: An Interdisciplinary Journal of Nonlinear Science, 2020-06: DOI: 10.1063/5.0006626

Books Global Bifurcations and Chaos -- Analytical Methods. Springer-Verlag Applied Mathematical Science Series. 1988, second printing 1990. ISBN 0387967753 Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer-Verlag textbooks in Applied Mathematics Series, 1990, second printing 1991. Second Edition (expanded) 2003. First edition translated into Japanese. ISBN 0387001778 Chaotic Transport in Dynamical Systems. Springer-Verlag Interdisciplinary Applied Mathematical Sciences Series, 1992. ISBN 0387975225 Global Dynamics, Phase Space Transport, Orbits Homoclinic to Resonances, and Applications. American Mathematical Society, 1993. ISBN 0821892029 Normally Hyperbolic Invariant Manifolds in Dynamical Systems. Springer-Verlag Applied Mathematical Science Series, 1994. ISBN 038794205X Invariant Manifolds and Fibrations for Perturbed Nonlinear Schrödinger Equations (with Y. Li). Springer-Verlag Applied Mathematical Science Series, 1997. ISBN 0387949259 Lagrangian Transport in Geophysical Jets and Waves: The Dynamical Systems Approach (with R. Samelson). Springer-Verlag Interdisciplinary Applied Mathematical Sciences Series, 2006. Translated into Russian, 2010. ISBN 0387332693 Mathematical Foundations of Mixing: The Linked Twist Map as a Paradigm in Applications Micro to Macro, Fluids to Solids (with R. Sturman and J. M. Ottino). Cambridge University Press, 2006. ISBN 0521868130

Open books Elementary Classical Mechanics. figshare. (2017) Ordinary Differential Equations. figshare. (2017) Solutions to the Exercises in Elementary Classical Mechanics. Figshare. (2018) Lagrangian Descriptors: Discovery and Quantification of Phase Space Structure and Transport Chemical Reactions: A Journey into Phase Space Wiggins, Stephen (2020): Elementary Quantum Mechanics. figshare. Book Wiggins, Stephen (2020): Solutions to the Exercises in Elementary Quantum Mechanics. figshare. Book

References

External links CHAMPS Project Google Scholar ORCID

Worked examples

Example 1 — a first encounter with Stephen Wiggins

Start with the simplest possible case. Write down what Stephen Wiggins claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Stephen Wiggins before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Stephen Wiggins ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Stephen Wiggins

In research: Stephen Wiggins appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Stephen Wiggins in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Stephen Wiggins is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1959 births, 20th-century American mathematicians, 20th-century American physicists, so understanding it makes those chapters shorter.
In everyday life: Look for Stephen Wiggins outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Stephen Wiggins in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Stephen Wiggins means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Stephen Wiggins out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Stephen Wiggins in simple terms?

Why does Stephen Wiggins matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Stephen Wiggins?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Stephen Wiggins.