My key result in this field is a constructive explanation of the Ziegler-Bottema paradox of destabilization by small dissipation of reversible and Hamiltonian systems [1]. It is based on the original perturbation technique that I have developed for the multiparameter families of non-self-adjoint boundary eigenvalue problems and its combination with the methods of singularity theory [2]. My results stimulated considerable research activity in engineering and physics and lead to identification of similar phenomena in seemingly unrelated applications [3-5].
[1] O.N. Kirillov (2005) A theory of the destabilization paradox in non-conservative systems. Acta Mechanica, 174(3-4): 145-166
[2] O.N. Kirillov (2010) Eigenvalue bifurcation in multiparameter families of non-self-adjoint operator matrices. Zeitschrift fur angewandte Mathemtik und Physik, 61(2): 221-234
[3] O.N. Kirillov, F. Verhulst (2010) Paradoxes of dissipation-induced destabilization or who opened Whitney’s umbrella? Zeitschrift fur angewandte Mathematik und Mechanik-ZAMM, 90(6): 462 – 488
[4] O.N. Kirillov, M.L. Overton (2013) Robust stability at the swallowtail singularity. Frontiers in Physics, 1: 24
[5] O.N. Kirillov (2013) Stabilizing and destabilizing perturbations of PT -symmetric indefinitely damped systems. Philosophical Transactions of the Royal Society A, 371: 20120051
Dr. Oleg N. Kirillov 