Semigroup dynamics for flight vectors
by Robert E. O'Brien
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 10, No. 4, 2020

Abstract: A commutative semigroup of contractions on a Hilbert space, , has a natural order and resultant net structure which defines stability, system dynamics, and α and ω limits for the flight vectors ₀. The space of 'pure' flight vectors - no nontrivial weakly stable components - are spanned by the ω limits of weakly-wandering vectors which are weakly Poisson recurrent. ₀ splits: ₀ = _m ⊕ _w, _w the weakly stable subspace and _m the weakly Poisson recurrent space. _m = ⊕M(x_τ, ) where M(x_τ, ) is the closed subspace spanned by the weak limit points of x_τ, {x_τ} an orthonormal set of weakly-wandering vectors in _m. Examples illustrate the results.

Online publication date: Thu, 20-Aug-2020

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