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First integrals for solutions of the conformal Mercator equation

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TWT - Twistor theory

In [Dunajski & Krynski 2021], a variational formulation for the conformal geodesic equation was introduced.  It was also shown in the same article that in the conformally flat case the same Lagrangian gives rise to a 4th order ODE called the conformal Mercator equation, to which conformal geodesics form a subclass of solutions.   In this talk, first integrals for solutions of the conformal Mercator equation derived using Noether’s principle and associated to conformal Killing vector fields will be discussed.

This talk is part of the Isaac Newton Institute Seminar Series series.

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