ITERATION OF QUADRATIC MAPS ON MATRIX ALGEBRAS-Reference-Cited by-同舟云学术

ITERATION OF QUADRATIC MAPS ON MATRIX ALGEBRAS

Published:2012-06 Issue:06 Volume:22 Page:1250150
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

NASCIMENTO BAPTISTA ALEXANDRA¹²,CORREIA RAMOS CARLOS³,MARTINS NUNO⁴

Affiliation:

1. Department of Mathematics, School of Technology and Management, Polytechnic Institute of Leiria, Campus 2, Morro do Lena – Alto do Vieiro, 2411-901, Leiria, Portugal

2. Centro de Investigação em Matemática e Aplicações, University of Évora, Rua Romão Ramalho, 59, 7000-671, Évora, Portugal

3. Centro de Investigação em Matemática e Aplicações, Department of Mathematics, University of Évora, Rua Romão Ramalho, 59, 7000-671, Évora, Portugal

4. Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Department of Mathematics, Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127412501507

Reference20 articles.

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4. Generalization of 3D Mandelbrot and Julia sets

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