Geodesic
An explanation to “Rolling simplexes and their commensurability” (field equations in accordance with Tycho Brahe)
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 4, pp. 193-215
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Various Cartesian models of central power fields with quadratic dynamics are studied. These examples lead the reader to comprehension of basic aspects of the differential algebraic-geometrical Brahe–Descartes–Wotton theory, which embraces central power fields whose dynamics is composed of flat affine algebraic curves of degree at most $N$ ($N=1,2,3,\dots$). When $N=2$, a quadratic rolling simplex law is proved by purely algebraic means. 
@article{FPM_2012_17_4_a11,
     author = {Yu. P. Razmyslov},
     title = {An explanation to {{\textquotedblleft}Rolling} simplexes and their commensurability{\textquotedblright} (field equations in accordance with {Tycho} {Brahe)}},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {193--215},
     year = {2012},
     volume = {17},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2012_17_4_a11/}
}
TY  - JOUR
AU  - Yu. P. Razmyslov
TI  - An explanation to “Rolling simplexes and their commensurability” (field equations in accordance with Tycho Brahe)
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2012
SP  - 193
EP  - 215
VL  - 17
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/FPM_2012_17_4_a11/
LA  - ru
ID  - FPM_2012_17_4_a11
ER  - 
%0 Journal Article
%A Yu. P. Razmyslov
%T An explanation to “Rolling simplexes and their commensurability” (field equations in accordance with Tycho Brahe)
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2012
%P 193-215
%V 17
%N 4
%U http://geodesic.mathdoc.fr/item/FPM_2012_17_4_a11/
%G ru
%F FPM_2012_17_4_a11
Yu. P. Razmyslov. An explanation to “Rolling simplexes and their commensurability” (field equations in accordance with Tycho Brahe). Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 4, pp. 193-215. http://geodesic.mathdoc.fr/item/FPM_2012_17_4_a11/

[1] Veil G., Klassicheskie gruppy. Ikh invarianty i predstavleniya, Izd. inostr. lit., M., 1947

[2] Gerasimova O. V., “Spektr kommutatornogo gamiltoniana vodorodopodoben”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 2008, no. 6, 71–74 | MR

[3] Gerasimova O. V., “Spektr kommutatornogo gamiltoniana srodni energeticheskim urovnyam atoma vodoroda”, Uspekhi mat. nauk, 64:4 (2009), 177–178 | DOI | MR | Zbl

[4] Efimovskaya O. V., Algebraicheskie aspekty teorii integriruemykh volchkov, Dis. $\dots$ kand. fiz.-mat. nauk, M., 2005

[5] Razmyslov Yu. P., “Rolling i soizmerimost simpleksov”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 2011, no. 5, 55–58 | MR

[6] Kaluza Th., “Zum Unitätsproblem der Physik”, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.), 1921, 966–972 | Zbl

[7] Petrogradsky V. M., Razmyslov Yu. P., Shishkin E. O., “Wreath products and Kaluzhnin–Krasner embedding for Lie algebras”, Proc. Am. Math. Soc., 135:3 (2007), 625–636 | DOI | MR | Zbl