Geodesic
An example of noncomputability of exponents of a system of ordinary differential equations
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2021), pp. 10-15 
A. V. Tiulenev. An example of noncomputability of exponents of a system of ordinary differential equations. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2021), pp. 10-15. http://geodesic.mathdoc.fr/item/VMUMM_2021_2_a1/
@article{VMUMM_2021_2_a1,
     author = {A. V. Tiulenev},
     title = {An example of noncomputability of exponents of a system of ordinary differential equations},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {10--15},
     year = {2021},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2021_2_a1/}
}
TY  - JOUR
AU  - A. V. Tiulenev
TI  - An example of noncomputability of exponents of a system of ordinary differential equations
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2021
SP  - 10
EP  - 15
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2021_2_a1/
LA  - ru
ID  - VMUMM_2021_2_a1
ER  - 
%0 Journal Article
%A A. V. Tiulenev
%T An example of noncomputability of exponents of a system of ordinary differential equations
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2021
%P 10-15
%N 2
%U http://geodesic.mathdoc.fr/item/VMUMM_2021_2_a1/
%G ru
%F VMUMM_2021_2_a1

Voir la notice de l'article provenant de la source Math-Net.Ru

A two-dimensional system of ordinary differential equations is constructed. The system possesses the following properties. The solution to a Cauchy problem with computable initial values is computable, the lower Lyapunov exponent is non-computable, the upper central exponent does not coincide with the higher Lyapunov exponent and is non-computable.

[1] Krupskii V.N., Plisko V.E., Teoriya algoritmov, Izdatelskii tsentr “Akademiya”, M., 2009

[2] Uspenskii V.A., Lektsii o vychislimykh funktsiyakh, Fizmatgiz, M., 1960

[3] Specker E., “Nicht konstructiv beweisbare Saetze der Analysis”, J. Symbol. Logic., 14:3 (1949), 145–158 | DOI | MR | Zbl

[4] Pour-El M.B., Richards J.I., Computability in Analysis and Physics, Springer-Verlag, Berlin–Heidelberg, 1989 | MR | Zbl

[5] Henrici P., Discrete variable methods in ordinary differential equations, Wiley, N.Y., 1962 | MR | Zbl

[6] Pour-El M.B., Richards J.I., “A computable ordinary differential equation which possesses no computable solution”, Ann. Math. Log., 17 (1979), 61–90 | DOI | MR | Zbl

[7] Bylov B.F., Vinograd R.E., Grobman D.M., Nemytskii V.V., Teoriya pokazatelei Lyapunova, Nauka, M., 1966