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A Galois D -groupoid for q -difference equations

Anne Granier (2011)

Annales de l’institut Fourier

We first recall Malgrange’s definition of D -groupoid and we define a Galois D -groupoid for q -difference equations. Then, we compute explicitly the Galois D -groupoid of a constant linear q -difference system, and show that it corresponds to the q -difference Galois group. Finally, we establish a conjugation between the Galois D -groupoids of two equivalent constant linear q -difference systems, and define a local Galois D -groupoid for Fuchsian linear q -difference systems by giving its realizations.

A general class of iterative equations on the unit circle

Marek Cezary Zdun, Wei Nian Zhang (2007)

Czechoslovak Mathematical Journal

A class of functional equations with nonlinear iterates is discussed on the unit circle 𝕋 1 . By lifting maps on 𝕋 1 and maps on the torus 𝕋 n to Euclidean spaces and extending their restrictions to a compact interval or cube, we prove existence, uniqueness and stability for their continuous solutions.

Currently displaying 61 – 80 of 355