Iteration of quadratic maps on matrix algebras

• Autor(es): Baptista, Alexandra Nascimento ; Ramos, Carlos Correia ; Martins, Nuno
• Data: 2012
• Identificador Persistente: http://hdl.handle.net/10174/7862
• Origem: Repositório Científico da Universidade de Évora
• Assunto(s): Matrix dynamics; iterated interval maps; noncommuting attractive cycles
• Tipo de Documento: Artigo
• Idioma: Inglês
• Editor(es): Chen, Guanrong (Ron)

Descrição

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.