Finite dimensional representations of ∗-algebras arising from a quadratic map

C. Correia Ramos, N. Martins and J. Sousa Ramos

Chaos, Solitons & Fractals, 2007, vol. 34, issue 4, 1202-1212

Abstract: Consider an operator X satisfying the algebraic relation XX∗=f(X∗X), where f is the one-parameter family of quadratic maps fb(x)=4bx(1−x) with b∈[0,1]. There is a correspondence between the periodic orbits of the dynamical system ([0,1],fb) and the unitary classes of matrices X satisfying XX∗=f(X∗X). Using the symbolic dynamics theory for interval maps, we describe in detail the combinatorial structure of the finite dimensional representations associated to this relation.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:34:y:2007:i:4:p:1202-1212

DOI: 10.1016/j.chaos.2006.03.113

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