On a general difference Galois theory II

Shuji Morikawa[1]; Hiroshi Umemura[1]

  • [1] Nagoya University Graduate School of Mathematics Nagoya (Japan)

Annales de l’institut Fourier (2009)

  • Volume: 59, Issue: 7, page 2733-2771
  • ISSN: 0373-0956

Abstract

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We apply the General Galois Theory of difference equations introduced in the first part to concrete examples. The General Galois Theory allows us to define a discrete dynamical system being infinitesimally solvable, which is a finer notion than being integrable. We determine all the infinitesimally solvable discrete dynamical systems on the compact Riemann surfaces.

How to cite

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Morikawa, Shuji, and Umemura, Hiroshi. "On a general difference Galois theory II." Annales de l’institut Fourier 59.7 (2009): 2733-2771. <http://eudml.org/doc/10470>.

@article{Morikawa2009,
abstract = {We apply the General Galois Theory of difference equations introduced in the first part to concrete examples. The General Galois Theory allows us to define a discrete dynamical system being infinitesimally solvable, which is a finer notion than being integrable. We determine all the infinitesimally solvable discrete dynamical systems on the compact Riemann surfaces.},
affiliation = {Nagoya University Graduate School of Mathematics Nagoya (Japan); Nagoya University Graduate School of Mathematics Nagoya (Japan)},
author = {Morikawa, Shuji, Umemura, Hiroshi},
journal = {Annales de l’institut Fourier},
keywords = {General difference Galois theory; dynamical system; integrable dynamical system; Galois groupoid; difference Galois theory; discrete dynamical system},
language = {eng},
number = {7},
pages = {2733-2771},
publisher = {Association des Annales de l’institut Fourier},
title = {On a general difference Galois theory II},
url = {http://eudml.org/doc/10470},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Morikawa, Shuji
AU - Umemura, Hiroshi
TI - On a general difference Galois theory II
JO - Annales de l’institut Fourier
PY - 2009
PB - Association des Annales de l’institut Fourier
VL - 59
IS - 7
SP - 2733
EP - 2771
AB - We apply the General Galois Theory of difference equations introduced in the first part to concrete examples. The General Galois Theory allows us to define a discrete dynamical system being infinitesimally solvable, which is a finer notion than being integrable. We determine all the infinitesimally solvable discrete dynamical systems on the compact Riemann surfaces.
LA - eng
KW - General difference Galois theory; dynamical system; integrable dynamical system; Galois groupoid; difference Galois theory; discrete dynamical system
UR - http://eudml.org/doc/10470
ER -

References

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  8. S. Morikawa, On a general Galois theory of difference equations I, Ann. Inst. Fourier, Grenoble (2010) 
  9. J. H. Silverman, The arithmetic of dynamical systems, 241 (2007), Springer, New York Zbl1130.37001MR2316407
  10. H. Umemura, Differential Galois theory of infinite dimension, Nagoya Math. J. 144 (1996), 59-135 Zbl0878.12002MR1425592
  11. H. Umemura, Galois theory and Painlevé equations, Théories asymptotiques et équations de Painlevé 14 (2006), 299-339, Soc. Math. France, Paris Zbl1156.34080MR2353471
  12. H. Umemura, Invitation to Galois theory, Differential equations and quantum groups 9 (2007), 269-289, Eur. Math. Soc., Zürich MR2322334
  13. H. Umemura, Sur l’équivalence des théories de Galois différentielles générales, C. R. Math. Acad. Sci. Paris 346 (2008), 1155-1158 Zbl1204.12009MR2464256
  14. H. Umemura, On the definition of Galois groupoid, Differential Equations and Singularities, 60 years of J.M. Aroca 323 (2010), Soc. Math. France Zbl1205.12005
  15. A. P. Veselov, Integrable mappings, Russian Math. Surveys 46 (1991), 1-51 Zbl0785.58027MR1160332

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