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Title: Iteration of quadratic maps on matrix algebras
Authors: Baptista, Alexandra Nascimento
Ramos, Carlos Correia
Martins, Nuno
Editors: Chen, Guanrong (Ron)
Keywords: Matrix dynamics
iterated interval maps
noncommuting attractive cycles
Issue Date: Jun-2012
Publisher: World Scientific Publishing Co
Citation: Nascimento Baptista, Alexandra; Correia Ramos, Carlos; Martins, Nuno Iteration of quadratic maps on matrix algebras. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 22 (2012), no. 6, 1250150, 7 pp.
Abstract: We study the iteration of a quadratic family in the algebra of 2 × 2 real matrices, parameterized by a matrix C. We analyze and classify the existing cycles (periodic orbits) and their dependence on the parameter matrix. We discuss how new dynamical phenomena occur as a consequence of the noncommutativity of the matrix product. In particular, we show that the commutator of the initial condition with parameter matrix C has a decisive role in the overall dynamics.
Type: article
Appears in Collections:MAT - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica
CIMA - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica

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