Paradoxes of dissipation-induced destabilization or who opened Whitney's umbrella?

Oleg Kirillov, Ferdinand Verhulst

Research output: Contribution to journalArticlepeer-review

84 Citations (Scopus)


The paradox of destabilization of a conservative or non-conservative system by small dissipation, or Ziegler's paradox (1952), has stimulated an ever growing interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations. Since the last decade it has been widely accepted that dissipation-induced instabilities are closely related to singularities arising on the stability boundary. What is less known is that the first complete explanation of Ziegler's paradox by means of the Whitney umbrella singularity dates back to 1956. We revisit this undeservedly forgotten pioneering result by Oene Bottema that outstripped later findings for about half a century. We discuss subsequent developments of the perturbation analysis of dissipation-induced instabilities and applications over this period, involving structural stability of matrices, Krein collision, Hamilton-Hopf bifurcation, and related bifurcations.
Original languageEnglish
Pages (from-to)462-488
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Issue number6
Publication statusPublished - 12 May 2010


Dive into the research topics of 'Paradoxes of dissipation-induced destabilization or who opened Whitney's umbrella?'. Together they form a unique fingerprint.

Cite this