THE DYNAMICS OF NQ-SYSTEMS IN THE PLANE-Reference-Cited by-同舟云学术

THE DYNAMICS OF NQ-SYSTEMS IN THE PLANE

Published:2009-01 Issue:01 Volume:19 Page:117-133
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

MENCINGER MATEJ¹²,KUTNJAK MILAN³

Affiliation:

1. Faculty of Civil Engineering, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia

2. IMFM, Jadranska 19, 1000 Ljubljana, Slovenia

3. Faculty of Electrical Engineering and Computer Science, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia

Abstract

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127409022786

Reference18 articles.

1. Iteration of Rational Functions

2. Dynamics of maps with nilpotent Jacobians

3. Nonassociative, real algebras and quadratic differential equations

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On a generalization of some instability results for Riccati equations via nonassociative algebras;Glasnik Matematicki;2022-12-30

2. Stability of the Planar Quadratic Systems from the Ring-Theoretic Viewpoint;Mathematics;2022-05-10

3. On (non)elementary singularities in Liénard systems;AIP Conference Proceedings;2017

4. Chaos in rational systems in the plane containing quadratic terms;Communications in Nonlinear Science and Numerical Simulation;2012-10

5. On Algebraic Approach in Quadratic Systems;International Journal of Mathematics and Mathematical Sciences;2011