Hendrik Broer

Hendrik Wolter Broer (born 18 February 1950, Diever) is a Dutch mathematician known for contributions to the theory of nonlinear dynamical systems.

Broer is well-known for having developed the parametrised Kolmogorov-Arnol’d-Moser (KAM) theory. This theory concerns the occurrence of invariant tori in dynamical systems depending on parameters,that carry multi- or quasi-periodic motions. This both goes for the conservative setting — like in celestial mechanics — and forthe dissipative setting where families of quasi-periodic tori may form the transitional interface between regular and chaotic dynamics. In the former context he worked on the Laplacian resonance in the motion of the Galilean satellites of Jupiter. In the latter he contributed to a better understanding of the topological and measure theoretical aspects of the Hopf-Landau-Lifschitz-Ruelle-Takens scenario for the onset of turbulence upon variation of parameters. The general non-degeneracy condition behind this theory is named after him and two of his colleagues.

He also contributed lto the general theory of bifurcations, for instance related to periodic motions that go through a resonance, thereby branching off subharmonic motions. Here both covering spaces and the corresponding equivariant singularity theory were introduced into the field of dynamical systems. Here also parametrised KAM theory comes into play.

Apart from developing theory, together with colleagues, he also worked on applications in the fields of classical and quantum mechanics, population dynamics and climate modelling. Here often computational tools were employed, which sometimes led to experimental mathematics.

Broer was granted a doctorate in the faculty of mathematics and natural sciences in 1979 under the supervision of Floris Takens for a thesis entitled Bifurcations of singularities in volume preserving vector fields.He was a professor at the University of Groningen, the Netherlands, from 1981 till his retirement in 2015.In 1985 he spent a semester as a guest professor of Boston University, Massachusetts.

In 2008 Broer became a member of the Royal Netherlands Academy of Arts and Sciences and in 2015 he was made a Knight of the Order of the Netherlands Lion.

• with G.B. Huitema, F. Takens and B.L.J. Braaksma. Unfoldings and bifurcations of quasi-periodic tori. Mems AMS 83 (421) (1990) pp 1–175
• with C. Simó and J. Puig. Resonance tongues and instability pockets in the quasi-periodic Hill-Schrödinger equation. Comm. Math. Phys. 241 (2003) 467-503
• with R.H. Cushman, F. Fassò and F. Takens. Geometry of KAM tori for nearly integrable Hamiltonian systems. Ergod. Th. & Dynam. Sys.27 (2007) 725-741
• with A.E. Sterk, R. Vitolo, C. Simó and H.A. Dijkstra. New nonlinear mechanisms in of midlatitude atmospheric low-frequency variability. Physica D: Nonlinear Phenomena 239 (2010) 701-718
• with K. Efstathiou. Uncovering fractional monodromy.Comm. Math. Phys. 324 (2013) 549-588
• Near-horizon celestial phenomena, a study in geometric optics. Acta Applicandæ Mathematicæ 137(1) (2015) 17-39
• With H. Jardón-Kojakhmetov and R. Roussarie. Analysis of a slow fast systems near a cusp singularity. Journ. Diff. Eqns. 260(4) (2016) 3785-3843
• with H. Hanßmann, On Jupiter and his Galilean satelites: librations of De Sitter’s periodic motions. Indag. Math. NS 27(5) 2016