Homoclinic attractors in discontinuos iterated function systems

被引：4

作者：

Lesniak, Krzysztof ^{[1
]}

机构：

[1] Nicolaus Copernicus Univ Torun, Fac Math & Comp Sci, PL-87100 Torun, Poland

来源：

CHAOS SOLITONS & FRACTALS | 2015年 / 81卷

关键词：

Iterated function system; Strict attractor; Hutchinson operator; Invariant set; Fast basin; FRACTALS; TIME;

D O I：

10.1016/j.chaos.2015.09.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Iterated function systems which consist of discontinuous maps are shown to be able to have attractors in the sense of Hutchinson. Moreover, it is demonstrated that discontinuous systems often admit strict attractors which are non-invariant, so one can call them homoclinic attractors. The existence of such attractors relates to the notion of a fast basin. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：146 / 149

页数：4

共 22 条

[11]

Jadczyk A., 2014, Quantum Fractals: From Heisenberg's Uncertainty to Barnsley's Fractality

[12]

Kieninger B., 2002, THESIS

[13]

Kolmogorov A. N., 1999, ELEMENTS THEORY FUNC

[14]

Lesniak K., 2003, Mathematica Slovaca, V53, P393

[15]

Mauldin R D., 2003, CAMB TRACT MATH, pp xii+281

[16] ATTRACTORS FOR CLOSED RELATIONS ON COMPACT HAUSDORFF SPACES [J].

MCGEHEE, R .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1992, 41 (04) :1165-1209

[17] Time-dependent iteration of random functions [J].

Mendivil, F. .

CHAOS SOLITONS & FRACTALS, 2015, 75 :178-184

[18]

Misiurewicz M, 2015, ERGOD THEORY DYN SYS

[19]

Mumford D., 2002, Indra's pearls. The vision of Felix Klein

[20] The shark teeth is a topological IFS-attractor [J].

Nowak, M. ;

Szarek, T. .

SIBERIAN MATHEMATICAL JOURNAL, 2014, 55 (02) :296-300

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