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.

引用

页数：7

共 25 条

[1]

[Anonymous], 1991, GRADUATE TEXTS MATH

[2]

Baptista A. N., 2010, P 12 INT C DIFF EQ A, P181

[3] ITERATION OF QUATERNION MAPS [J].

BEDDING, S ;

BRIGGS, K .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1995, 5 (03) :877-881

[4]

Bogush A. A., 2001, P 9 ANN SEM NPCS 200, P304

[5] Generalized Mandelbrot sets for meromorphic complex and quaternionic maps [J].

Buchanan, W ;

Gomatam, J ;

Steves, B .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2002, 12 (08) :1755-1777

[6] Generalization of 3D Mandelbrot and Julia sets [J].

Cheng Jin ;

Tan Jian-rong .

JOURNAL OF ZHEJIANG UNIVERSITY-SCIENCE A, 2007, 8 (01) :134-141

[7]

DOUADY A, 1985, ANN SCI ECOLE NORM S, V18, P287

[8] Artist's statement CQUATS - a non-distributive quad algebra for 3D renderings of Mandelbrot and Julia sets [J].

Gintz, TW .

COMPUTERS & GRAPHICS-UK, 2002, 26 (02) :367-370

[9]

Gomatam J, 1999, DISCRET CONTIN DYN S, V5, P107

[10] GENERALIZATION OF THE MANDELBROT SET - QUATERNIONIC QUADRATIC MAPS [J].

GOMATAM, J ;

DOYLE, J ;

STEVES, B ;

MCFARLANE, I .

CHAOS SOLITONS & FRACTALS, 1995, 5 (06) :971-986

← 1 2 3 →