Geodesic
Unimodular invariance of karyon decompositions of algebraic numbers in multidimensional continued fractions
Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 1, Tome 469 (2018), pp. 96-137 Cet article a éte moissonné depuis la source Math-Net.Ru

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By the differentiation method of induced toric tilins we find periodic expansions for algebraic irrationalities in multidimensional continued fractions. These expansions give the best karyon approximations with respect to polyhedral norms. The above irrationalities are obtained by the composition of backward continued fraction mappings and unimodular transformations of algebraic units that decompose into a purely periodic continued fractions. The artifact of this expansion several invariants has become: recurrence relations for numerators and denominators of convergent fractions and the rate of multidimensional approximation of irrationalities by rational numbers. 
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V. G. Zhuravlev. Unimodular invariance of karyon decompositions of algebraic numbers in multidimensional continued fractions. Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 1, Tome 469 (2018), pp. 96-137. http://geodesic.mathdoc.fr/item/ZNSL_2018_469_a3/

[1] V. G. Zhuravlev, “Differentsirovanie indutsirovannykh razbienii tora i mnogomernye priblizheniya algebraicheskikh chisel”, Zap. nauchn. semin. POMI, 445, 2016, 33–92 | MR

[2] A. Ya. Khinchin, Tsepnye drobi, chetvertoe izd., Nauka, M., 1978

[3] V. G. Zhuravlev, “Periodicheskie yadernye razlozheniya edinits algebraicheskikh polei v tsepnye drobi”, Zap. nauchn. semin. POMI, 449, 2016, 84–129 | MR

[4] V. G. Zhuravlev, “Dvumernye priblizheniya metodom delyaschikhsya toricheskikh razbienii”, Zap. nauchn. semin. POMI, 440, 2015, 81–98 | MR

[5] V. G. Zhuravlev, “Delyaschiesya razbieniya tora i mnozhestva ogranichennogo ostatka”, Zap. nauchn. semin. POMI, 440, 2015, 99–122 | MR

[6] V. G. Zhuravlev, “Periodicheskie yadernye razlozheniya kubicheskikh irratsionalnostei v tsepnye drobi”, Sovr. probl. matem., 23, MIAN, M., 2016, 43–68 | DOI

[7] Z. Coelho, A. Lopes, L. F. Da Rocha, “Absolutely Continuous Invariant Measures for a Class of Affine Interval Exchange Maps”, Proccedings of The American Mathematical Society, 123:11 (1995), 3533–3542 | DOI | MR | Zbl

[8] V. G. Zhuravlev, A. V. Shutov, “Derivaties of circle rotations and similarity of orbits”, Max-Planck-Institut für Mathematik Preprint Series, 62 (2004), 1–11 | MR

[9] M. Furukado, Sh. Ito, A. Saito, J. Tamura, Sh. Yasutomi, “A new multidimensional slow continued fraction algorithm and stepped surface”, Experemental Mathematics, 23:4 (2014), 390–410 | DOI | MR | Zbl

[10] V. G. Zhuravlev, “Mnogogranniki ogranichennogo ostatka”, Matematika i informatika, K 75-letiyu so dnya rozhdeniya Anatoliya Alekseevicha Karatsuby, v. 1, Sovr. probl. matem., 16, MIAN, M., 2012, 82–102 | DOI | Zbl

[11] V. G. Zhuravlev, “Perekladyvayuschiesya toricheskie razvertki i mnozhestva ogranichennogo ostatka”, Zap. nauchn. semin. POMI, 392, 2011, 95–145

[12] E. S. Fedorov, Nachala ucheniya o figurakh, M., 1953 | MR

[13] G. F. Voronoi, Sobranie sochinenii, v. 2, Kiev, 1952

[14] V. G. Zhuravlev, “Razbieniya Rozi i mnozhestva ogranichennogo ostatka”, Zap. nauchn. semin. POMI, 322, 2005, 83–106 | MR | Zbl