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Singularities in Poisson manifolds: bifurcation and symmetry breaking

Hamiltonian systems, from topology to applications through analysis II November 26, 2018 - November 30, 2018

November 28, 2018 (09:30 AM PST - 10:30 AM PST)
Speaker(s): Zensho Yoshida (University of Tokyo)
Location: MSRI: Simons Auditorium
  • Poisson algebra

  • singularities

  • chirality

  • bifurcation

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification



A variety of interesting structures and dynamics stem from singularities of Poisson operators. As well known, the kernel of a finite-dimensional Poisson operator can be integrated “locally” to define Casimirs, and their level-sets foliate the phase space yielding symplectic submanifolds (Lie-Darboux theorem). However, the global structure can be more complex when the Poisson operator has “singularities” where its rank changes. Invoking some physical examples (both finite dimensional and infinite dimensional), we discuss how singularities cause seemingly non-Hamiltonian phenomena. Some theoretical methods for probing into singularities will be also introduced.

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