Iteration of quadratic maps on matrix algebras

• Author(s): Baptista, Alexandra Nascimento ; Ramos, Carlos Correia ; Martins, Nuno
• Date: 2012
• Persistent ID: http://hdl.handle.net/10174/7862
• Origin: Repositório Científico da Universidade de Évora
• Subject(s): Matrix dynamics; iterated interval maps; noncommuting attractive cycles
• Document Type: Article
• Language: English
• Editor(s): Chen, Guanrong (Ron)

Description

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.