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Preprint . 2018
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Science China Mathematics
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https://dx.doi.org/10.48550/ar...
Article . 2018
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Stable and non-symmetric pitchfork bifurcations

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 20 Aug 2020Embargo end date: 01 Jan 2018 English Publisher:Springer Science and Business Media LLCJournal:Science China Mathematics, volume 63, pages 1,837-1,852 (issn: 1674-7283, eissn: 1869-1862, Copyright policy )
Authors: Michael Shub; Yun Yang; Enrique R. Pujals;

doi: 10.1007/s11425-019-1758-5 , 10.48550/arxiv.1804.03264

arXiv: http://arxiv.org/abs/1804.03264

Stable and non-symmetric pitchfork bifurcations

Abstract

In this paper, we present a criterion for pitchfork bifurcation of smooth vector fields based on a topological argument. Our result expands Rajapakse and Smale's result \cite{RS2} significantly. Based on our criterion, we present a class of families of non-symmetric vector fields undergoing a pitchfork bifurcation.

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Keywords

FOS: Mathematics, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, 37G10, 37G40

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Average
Average
Green
bronze