Painlevé VI equations in p-adic time
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Using the description of Painlevé VI family of differential equations in terms of a universal elliptic curve, going back to R. Fuchs, we translate it into the realm of Buium’s p-adic Arithmetic Differential Equations, where the role of derivative is played by a version of Fermat quotient.
KeywordsPainlevé VI p-adic derivations Hamiltonian
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