Dynamics in the transition case invertible/non-invertible in a 2D Piecewise Linear Map

Laura Gardini and Wirot Tikjha

Chaos, Solitons & Fractals, 2020, vol. 137, issue C

Abstract: We consider the dynamics of a family of two-dimensional piecewise linear maps at the transition between the invertible and non-invertible cases. This leads to a degeneracy consisting of a half plane which is mapped onto a straight line, the critical line LC. In these regimes the ω-limit set of the trajectories must be on the images of some segment of LC. Thus, the first return map along this line can help in defining the global dynamic behavior of the two-dimensional map. In other cases, the first return map helps in determining some attracting sets, although not the unique attractors of the two-dimensional map.

Keywords: Two-dimensional piecewise linear maps; non-invertibility; first return map; infinitely many inverses; maps of type Z0−Z1−Z∞ (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077920302137
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:137:y:2020:i:c:s0960077920302137

DOI: 10.1016/j.chaos.2020.109813

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().