CRM: Centro De Giorgi
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Probabilistic methods in dynamics

New Hidden Symmetries in Equivariant Dynamical Systems

speaker: Michael Dellnitz (Padeborn University)

abstract: We investigate matrices A ∈ R n,n with respect to their equivariance proper- ties: It is well known that the equivariance of A with respect to certain groups Σ ⊂ O(n) generically leads to the existence of multiple eigenvalues. We show that in this case A is (additionally) equivariant with respect to the action of a group Γ(A) 'Qk i=1 O(mi) where m1, . . . , mk are the multiplicities of the eigen- values λ1, . . . , λk of A – even if Σ is finite. Moreover, Γ(A) consists of all the matrices which commute with A, so that in particular Σ ⊂ Γ(A). We discuss implications of this result for equivariant nonlinear dynamical systems. This way we are able to explain the existence of solutions of certain types which is induced by the action of ”hidden symmetries” in Γ(A) \ Σ. This is joint work with Raphael Gerlach (Paderborn University) and S ̈oren von der Gracht (Paderborn University).

Wed 31 May, 17:00 - 17:50, Aula Dini


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