Generic Singularities of 3D Piecewise Smooth Dynamical Systems

Marco Antonio Teixeira () and Otávio M. L. Gomide
Additional contact information
Marco Antonio Teixeira: University of Campinas, Institute of Mathematics, Statistics and Scientific Computing
Otávio M. L. Gomide: University of Campinas, Institute of Mathematics, Statistics and Scientific Computing

A chapter in Advances in Mathematics and Applications, 2018, pp 373-404 from Springer

Abstract: Abstract The aim of this paper is to provide a discussion on the current directions of research involving typical singularities of 3D nonsmooth vector fields. A brief survey of known results is also presented. We describe the dynamical features of a fold–fold singularity in its most basic form and we give a complete and detailed proof of its local structural stability (or instability). In addition, classes of all topological types of a fold–fold singularity are intrinsically characterized. Such proof essentially follows from some lines laid out by Colombo, García, Jeffrey, Teixeira, and others and it offers a rigorous mathematical treatment under clear and crisp assumptions and solid arguments. One should highlight that the geometric–topological methods employed lead us to the mathematical understanding of the dynamics around a T-singularity. This approach lends itself to applications in generic bifurcation theory. It is worth to say that such subject is still poorly understood in higher dimension.

Date: 2018
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

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:spr:sprchp:978-3-319-94015-1_15

Ordering information: This item can be ordered from
http://www.springer.com/9783319940151

DOI: 10.1007/978-3-319-94015-1_15

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().