The leading exponential growth rates of all singular values and eigenvalue moduli of PSp(4,R) Hitchin holonomies along quartic rays are explicit integrals of fourth roots of the quartic differential over saddle connections.
Good wild harmonic bundles and good filtered Higgs bundles
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Holonomy Asymptotics along Quartic Differential Rays
The leading exponential growth rates of all singular values and eigenvalue moduli of PSp(4,R) Hitchin holonomies along quartic rays are explicit integrals of fourth roots of the quartic differential over saddle connections.