Department of Mathematics

Analysis and PDE

  •  Richard Kollar, Comenius University, Bratislava, Slovakia
  •  Krein signature - three unexpected lessons
  •  09/19/2018
  •  4:10 PM - 5:00 PM
  •  C517 Wells Hall

Krein signature is an algebraic quantity characterizing purely imaginary eigenvalues of linearized Hamiltonian systems. Instabilities growing from a stable state in these systems are caused by Hamiltonian-Hopf bifurcations, i.e. events when two purely imaginary eigenvalues collide and split off the imaginary axis. The necessary condition for such an event is that the colliding eigenvalues must have mixed signature. In the talk we present three elegant results related to Krein signature - graphical Krein signature and its use to simplify proofs, a connection to stability in general extended systems, and ability to characterize the nature of the eigenvalue collisions directly from the reduced dispersion relation.

 

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Department of Mathematics
Michigan State University
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