Differential and Integral Equations

Not every conjugate point of a semi-Riemannian geodesic is a bifurcation point

Giacomo Marchesi, Alessandro Portaluri, and Nils Waterstraat

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Abstract

We revisit an example of a semi-Riemannian geodesic that was discussed by Musso, Pejsachowicz and Portaluri in 2007 to show that not every conjugate point is a bifurcation point. We point out a mistake in their argument, showing that on this geodesic actually every conjugate point is a bifurcation point. Finally, we provide an improved example which shows that the claim in our title is nevertheless true.

Article information

Source
Differential Integral Equations, Volume 31, Number 11/12 (2018), 871-880.

Dates
First available in Project Euclid: 25 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.die/1537840873

Mathematical Reviews number (MathSciNet)
MR3857868

Zentralblatt MATH identifier
06986982

Subjects
Primary: 58E07: Abstract bifurcation theory 58E10: Applications to the theory of geodesics (problems in one independent variable) 34C23: Bifurcation [See also 37Gxx]

Citation

Marchesi, Giacomo; Portaluri, Alessandro; Waterstraat, Nils. Not every conjugate point of a semi-Riemannian geodesic is a bifurcation point. Differential Integral Equations 31 (2018), no. 11/12, 871--880. https://projecteuclid.org/euclid.die/1537840873


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