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Stable and non-symmetric pitchfork bifurcations

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In this paper, we present a criterion for pitchfork bifurcations of smooth vector fields based on a topological argument. Our result expands Rajapakse and Smale℉s result [15] significantly. Based on our criterion, we present a class of families of non-symmetric vector fields undergoing a pitchfork bifurcation.

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The second author was supported by the Smale Institute. This work was finished during the third author℉s stay in Graduate Center of City University of New York.

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Correspondence to Michael Shub.

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In Memory of Professor Shantao Liao

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Pujals, E., Shub, M. & Yang, Y. Stable and non-symmetric pitchfork bifurcations. Sci. China Math. 63, 1837–1852 (2020).

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