The Briggs–Bers criterion is a mathematical criterion used in the study of complex dynamics, particularly in the context of the iteration of functions. It specifically pertains to the behavior of holomorphic functions or rational functions on the Riemann sphere, focusing on the conditions under which certain types of dynamical systems exhibit specific behaviors, such as the presence of non-escaping points or the structure of their Julia sets.
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A criterion for absolute wave-packet instability based on analytic continuation of the spatial roots of a dispersion relation. Start the temporal inversion contour above the spectrum, then lower it while deforming the spatial contour. A spatial pinch point occurs when branches originating in opposite spatial half-planes obstruct that deformation. A double root is only an algebraic candidate. The opposite-half-plane condition is stated in the primary study doi.org/10.1017/jfm.2016.195, section 4.2.