Isolated singularities of Toda equations and cyclic Higgs bundles

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Abstract: This paper is the second part of our study on the Toda equations and the cyclic Higgs bundles associated to

r

-differentials over non-compact Riemann surfaces. We classify all the solutions up to boundedness around the isolated singularity of an

r

-differential under the assumption that the

r

-differential is meromorphic or has some type of essential singularity. As a result, for example, we classify all the solutions on

m a t h b b C

if the

r

-differential is a finite sum of the exponential of polynomials.

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