ERGODIC PROPERTIES OF PIECEWISE-LINEAR MAPS ON FRACTAL REPELLERS

被引：24

作者：

TASAKI, S ^{[1
]}

SUCHANECKI, Z ^{[1
]}

ANTONIOU, I ^{[1
]}

机构：

[1] FREE UNIV BRUSSELS,FAC SCI,B-1050 BRUSSELS,BELGIUM

来源：

PHYSICS LETTERS A | 1993年 / 179卷 / 02期

关键词：

D O I：

10.1016/0375-9601(93)90657-L

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We construct a class of one-dimensional piecewise linear maps admitting fractal invariant sets and uncountably many invariant measures and show that they are ergodic (exact). A physical measure is selected as the invariant measure with maximum information dimension. We also briefly discuss the spectral decomposition of the Frobenius-Perron operator.

引用

页码：103 / 110

页数：8

共 40 条

[1] SPECTRAL DECOMPOSITION OF THE RENYI MAP
ANTONIOU, I
TASAKI, S
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1993, 26 (01): : 73 - 94
[2] ANTONIOU I, UNPUB
[3] Boas R. P., 1964, POLYNOMIAL EXPANSION
[4] THE ENTROPY FUNCTION FOR CHARACTERISTIC EXPONENTS
BOHR, T
RAND, D
[J]. PHYSICA D, 1987, 25 (1-3): : 387 - 398
[5] BOWEN R, 1975, LECTURE NOTES MATH, V470
[6] de Rham G., 1956, REND SEM MAT TORINO, V16, P101
[7] ERGODIC-THEORY OF CHAOS AND STRANGE ATTRACTORS
ECKMANN, JP
RUELLE, D
[J]. REVIEWS OF MODERN PHYSICS, 1985, 57 (03) : 617 - 656
[8] SCALING PROPERTIES OF MULTIFRACTALS AS AN EIGENVALUE PROBLEM
FEIGENBAUM, MJ
PROCACCIA, I
TEL, T
[J]. PHYSICAL REVIEW A, 1989, 39 (10): : 5359 - 5372
[9] DIFFUSION, EFFUSION, AND CHAOTIC SCATTERING - AN EXACTLY SOLVABLE LIOUVILLIAN DYNAMICS
GASPARD, P
[J]. JOURNAL OF STATISTICAL PHYSICS, 1992, 68 (5-6) : 673 - 747
[10] DIFFUSION IN UNIFORMLY HYPERBOLIC ONE-DIMENSIONAL MAPS AND APPELL POLYNOMIALS
GASPARD, P
[J]. PHYSICS LETTERS A, 1992, 168 (01) : 13 - 17

← 1 2 3 4 →