Plane maps with denominator. I. Some generic properties

被引：58

作者：

Bischi, GI ^{[1
]}

Gardini, L

Mira, C

机构：

[1] Univ Urbino, Ist Sci Econ, I-61029 Urbino, Italy

[2] Univ Parma, Ist Matemat Levi, I-43100 Parma, Italy

[3] Inst Natl Sci Appl, Grp Etud Syst Non Lineaires & Applicat, Complexe Sci Rangueil, F-31077 Toulouse, France

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 1999年 / 9卷 / 01期

关键词：

D O I：

10.1142/S0218127499000079

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is devoted to the study of some global dynamical properties and bifurcations of two-dimensional maps related to the presence, in the map or in one of its inverses, of a vanishing denominator. The new concepts of focal points and of prefocal curves are introduced in order to characterize some new kinds of contact bifurcations specific to maps with denominator. The occurrence of such bifurcations gives rise to new dynamic phenomena, and new structures of basin boundaries and invariant sets, whose presence can only be observed if a map (or some of its inverses) has a vanishing denominator.

引用

页码：119 / 153

页数：35

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