ITERATION OF QUADRATIC MAPS ON MATRIX ALGEBRAS

被引：3
作者：
Baptista, Alexandra Nascimento [1 ,2 ]
Ramos, Carlos Correia [2 ]
Martins, Nuno [3 ]
机构：
[1] Polytech Inst Leiria, Sch Technol & Management, Dept Math, P-2411901 Leiria, Portugal
[2] Univ Evora, Ctr Invest Matemat & Aplicacoes, P-7000671 Evora, Portugal
[3] Univ Tecn Lisboa, Inst Super Tecn, Dept Math, Ctr Anal Matemat Geometria & Sistemas Dinam, P-1049001 Lisbon, Portugal
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2012年 / 22卷 / 06期
关键词：
Matrix dynamics; iterated interval maps; noncommuting attractive cycles; MANDELBROT SET; DYNAMICS;
D O I：
10.1142/S0218127412501507
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the iteration of a quadratic family in the algebra of 2x2 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.
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页数：7
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