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Using a navigation process with the datum $(F,V)$, in which $F$ is a Finslermetric and the smooth tangent vector field $V$ satisfies $F(-V(x))>1$everywhere, a Lorentz Finsler metric $\tilde{F}$ can be induced. Isoparametricfunctions and isoparametric hypersurfaces with or without involving a smoothmeasure can be defined for $\tilde{F}$. When the vector field $V$ in thenavigation datum is homothetic, we prove the local correspondences betweenisoparametric functions and isoparametric hypersurfaces before and after thisnavigation process. Using these correspondences, we provide some examples ofisoparametric functions and isoparametric hypersurfaces on a Funk space ofLorentz Randers type.

Isoparametric hypersurfaces induced by navigation in Lorentz Finsler geometry