THE DYNAMICS OF NQ-SYSTEMS IN THE PLANE

被引：5
作者：
Mencinger, Matej [1 ,2 ]
Kutnjak, Milan [3 ]
机构：
[1] Univ Maribor, Fac Civil Engn, SLO-2000 Maribor, Slovenia
[2] IMFM, Ljubljana 1000, Slovenia
[3] Univ Maribor, Fac Elect Engn & Comp Sci, SLO-2000 Maribor, Slovenia
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2009年 / 19卷 / 01期
关键词：
Homogeneous system; quadratic system; discrete dynamical system; nilpotent; commutative algebra; nonassociative algebra; ALGEBRAS; STABILITY; ODES; MAPS;
D O I：
10.1142/S0218127409022786
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The dynamics of discrete homogeneous quadratic planar maps is considered via the algebraic approach. There is a one-to-one correspondence between these systems and 2D commutative algebras (c.f. [Markus, 1960]). In particular, we consider the systems corresponding to algebras which contain some nilpotents of rank two (i.e. NQ-systems). Markus algebraic classification is used to obtain the class representatives. The case-by-case dynamical analysis is presented. It is proven that there is no chaos in NQ-systems. Yet, some cases are really interesting from the dynamical and bifurcational points of view.
引用
收藏
页码：117 / 133
页数：17
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