Henk Broer

Key takeaways

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

Reference excerpt

Hendrik Wolter Broer (18 February 1950) is a Dutch mathematician working in the field of nonlinear dynamical systems. Most of his work concerns fundamental aspects of the theory. He is most noted for his research regarding bifurcations (or phase transitions) involving multi- or quasi-periodicity.

Biography Henk Broer was born in Diever in 1950. From 1967 on he studied mathematics and physics at the University of Groningen, where he got his MSc in 1974 and his PhD degree in 1979. In 1980 he was appointed assistant professor at the mathematics department of the University of Groningen. In 1991 he became professor of dynamical systems. He was managing director of the Dutch Research Council (NOW) based research cluster Nonlinear Dynamics of Natural Systems (NDNS), that united all dynamical systems research in the Netherlands. The first semester of 1985 he was visiting professor at Boston University. He held short term positions at the Universitat de Barcelona (Spain), at the Université de Bourgogne (Dijon, France), at the Georgia Institute of Technology (Atlanta, USA) and the Universidade Federal do Rio de Janeiro (IFRJ) / Instituto Matemática Pura e Aplicada (IMPA) in Rio de Janeiro (Brazil). He served a term as chairperson of the mathematics chamber of the Association of Universities in the Netherlands (VSNU) and of the Royal Dutch Mathematical Society (Koninklijk Wiskundig Genootschap). In these two administrative duties he contributed to the unification of the Dutch mathematicians in their contacts with the Dutch government. He also was one of the founders of the Dutch inter-university masterprogramme Mastermath. In 2008 he became a member of the Royal Netherlands Academy of Arts and Sciences (Koninklijke Nederlandse Akademie voor Kunsten en Wetenschappen - KNAW), where he served a term as chairperson of the section Mathematics. He was a long term managing editor of the Dutch journal Indagationes Mathematicæ. In 2015 he became emeritus professor.

Research contributions In his PhD thesis, Broer worked on bifurcations of singularities in volume preserving vector fields, where he discovered quasi-periodic invariant tori for the first time. This was the starting point of a large scale inventory of occurrences: together with his school he set up a supporting theory of bifurcating tori, thereby combining singularity theory with the Kolmogorov-Arnold-Moser (KAM) theory 1 as reported in 2, 3 and 4. (Numbers refer to works under Selected publications.) Broer also worked on geometrically inspired or computationally assisted results 5, 6, 7, 8, 9 , 10 and 11, some including applications to modeling. (ibid.)

Awards and honors Broer became a member of the Royal Netherlands Academy of Arts and Sciences (KNAW) in 2008. At the international conference Mathematical Analysis and Applications of 2024 in Porto he obtained a career award for applications of analysis in the theory of dynamical systems. At his retirement in 2015 he was appointed knight of the order of the Netherlands lion.

Selected publications H.W. Broer, KAM theory: the legacy of Kolmogorov’s 1954 paper. Bulletin of the American Mathematical Society 41(4) (2004) 507-521. doi:10.1090/S0273-0979-04-01009-2 H.W. Broer, G.B. Huitema and M.B. Sevryuk, Quasi-periodic tori in families of dynamical systems: order amidst chaos. Lecture Notes in Mathematics 1645 Springer Verlag 1996. doi:10.1007/978-3-540-49613-7 H.W. Broer and F. Takens, Dynamical Systems and Chaos. Applied Mathematical Sciences 172 Springer Verlag 2011. doi:10.1007/978-1-4419-6870-8; Hardcover ISBN 978-1-4419-6869-2; Softcover ISBN 978-1-4614-2712-4 H.W. Broer, G.B. Huitema, F. Takens and B.L.J. Braaksma, Unfoldings and bifurcations of quasi-periodic tori. Mem AMS 83(421) American Mathematical Society 1990. eBook ISBN 978-1-4704-0844-2 H.W. Broer, H. Hanßmann, On Jupiter and his Galilean satellites: librations of De Sitter’s periodic motions. Indag Math NS 27(5) 1305-1337 (2016). doi:10.1016/j.indag.2016.09.002 K. Efstathiou and H.W. Broer, Uncovering fractional monodromy. Commun. Math. Phys. 324 (549-588) (2013). doi:10.1007/s00220-013-1816-9 H.W. Broer, C. Simó, R. Vitolo, Bifurcations and strange attractors in the Lorenz-84 climate model with seasonal forcing. Nonlinearity 15(4) (2002) 1205-1267. doi:10.1088/0951-7715/15/4/312 H.W. Broer and C. Simó, Resonance tongues in Hill’s equations: a geometric approach. Journ. Diff. Eqns. 166 290-327 (2000). doi:10.1006/jdeq.2000.3804 H.W. Broer, C. Simó and J.C. Tatjer, Towards global models near homoclinic tangencies of dissipative diffeomorphisms. Nonlinearity 11(3) (1998) 667-770. doi:10.1088/0951-7715/11/3/015 H.W. Broer and F.M. Tangerman, From a differentiable to a real analytic perturbation theory, applications to the Kupka Smale theorems Ergod. Th. & Dynam. Sys. 6 345-362 (1986). doi:10.1017/S0143385700003540 H.W. Broer and G. Vegter, Subordinate Sil’nikov bifurcations near some singularities of vector fields having low codimension. Ergod. Th. & Dynam. Sys. 4 509-525 (1984). doi:10.1017/S0143385700002613

References

External links Henk Broer at the Mathematics Genealogy Project Official website ORCID 0000-0002-4009-7121 Henk Broer publications indexed by Google Scholar Publications by Henk Broer at ResearchGate J.K. Moser, Convergent series expansions for quasi-periodic motions. Mathematische Annalen 169 (1967) 136-176. Document at eudml.org E. Zehnder, Generalized implicit function theorems with applications to some small divisor problems, I and II. Comm. Pure Applied Mathematics 28 (1975) 91-140; 29 (1976) 49-111 doi:10.1002/cpa.3160280104

Illustrations

Worked examples

Example 1 — a first encounter with Henk Broer

Start with the simplest possible case. Write down what Henk Broer claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 Henk Broer 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 Henk Broer 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 Henk Broer

In research: Henk Broer appears in astronomy 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 Henk Broer 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: Henk Broer is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1950 births, Academic staff of the University of Groningen, Dutch mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Henk Broer 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.

How to study Henk Broer in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Henk Broer 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 Henk Broer out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Henk Broer in simple terms?

Hendrik Wolter Broer (18 February 1950) is a Dutch mathematician working in the field of nonlinear dynamical systems. Most of his work concerns fundamental aspects of the theory.

Why does Henk Broer matter?

Because it connects several astronomy 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 Henk Broer?

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 Henk Broer.