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.
Asymptotics of Higgs bundles in the Hitchin component
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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.