Difference Galois Theory for the “Applied” Mathematician

Vizio, Lucia Di

doi:10.1007/978-3-030-66249-3_2

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Elements Of Galois Theory Of Difference Equations1

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2021

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“…The setting considered here (as well as the notation) matches the approach developed in [DV19, §2 to §5], so we are going to refer to it. The only difference with [DV19] is that our field of constants C is algebraically closed. For this reason we can naively identify the Galois groups with their C-points, which makes things slightly easier.…”

Section: Elements Of Galois Theory Of Difference Equationsmentioning

confidence: 99%

A Galoisian proof of Ritt theorem on the differential transcendence of Poincaré functions

Di Vizio,

Fernandes

2021

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Using Galois theory of functional equations, we give a new proof of the main result of the paper "Transcendental transcendency of certain functions of Poincaré" by J.F. Ritt, on the differential transcendence of the solutions of the functional equation R(y(t)) = y(qt), where R(t) ∈ C(t) verifies R(0) = 0, R ′ (0) = q ∈ C, with |q| > 1. We also give a partial result in the case of an algebraic function R.

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Section: Elements Of Galois Theory Of Difference Equationsmentioning

confidence: 99%