ON THE DYNAMICS OF REAL POLYNOMIALS ON THE PLANE

被引：7

作者：

LOPES, AO ^{[1
]}

机构：

[1] UNIV FED RIO GRANDE SUL,INTITUTO MATEMAT,BR-91500 PORTO ALEGRE,RS,BRAZIL

来源：

COMPUTERS & GRAPHICS | 1992年 / 16卷 / 01期

关键词：

D O I：

10.1016/0097-8493(92)90066-5

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We analyze the dynamics of the map f(z) = z2 - szBAR where s is-an-element-of C is a constant and z is-an-element-of C is a variable. For some values of s, we can have invariant measures of density with respect to the two-dimensional Lebesgue measure. For other values of s we can have fractal repellers or the X-trange attractor. This problem is related to a Triple Point Phase Transition Model (Potts Model).

引用

页码：15 / 23

页数：9

共 15 条

[1]

[Anonymous], 1986, BEAUTY FRACTALS IMAG

[2]

BEDFORD E, 1990, INVENTIONES MATH, V87

[3]

Collet P., 1980, ITERATED MAPS INTERV

[4]

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

[5]

Falconer KJ., 1985, GEOMETRY FRACTAL SET, DOI 10.1017/CBO9780511623738

[6] QUANTITATIVE UNIVERSALITY FOR A CLASS OF NON-LINEAR TRANSFORMATIONS [J].

FEIGENBAUM, MJ .

JOURNAL OF STATISTICAL PHYSICS, 1978, 19 (01) :25-52

[7] DYNAMICAL PROPERTIES OF PLANE POLYNOMIAL AUTOMORPHISMS [J].

FRIEDLAND, S ;

MILNOR, J .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1989, 9 :67-99

[8] 2-DIMENSIONAL MAPPING WITH A STRANGE ATTRACTOR [J].

HENON, M .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1976, 50 (01) :69-77

[9] GENERALIZED TSCHEBYSCHEFF POLYNOMIALS ASSOCIATED WITH AFFINE WEYL GROUPS [J].

HOFFMAN, ME ;

WITHERS, WD .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 308 (01) :91-104

[10] DYNAMICS OF REAL POLYNOMIALS ON THE PLANE AND TRIPLE POINT PHASE-TRANSITION [J].

LOPES, AO .

MATHEMATICAL AND COMPUTER MODELLING, 1990, 13 (09) :17-32

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