Abstract
It is shown that central exponents of a local diffeomorpliism of a Riemannian manifold treated as functions on the direct product of the manifold and the space of its local diffeomorphisms with C1-compact-open topology belong to the fourth Baire class.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V. M. Millionshchikov, “Typical Properties of Conditional Exponential Stability. Part VIII,” Differ. Uravn. 20 (11), 1889 (1984).
V. M. Millionshchikov, “Lyapunov Exponents of a Family of Endomorphisms of a Metrized Vector Bundle,” Matem. Zametki 38 (1), 92 (1985).
M. W. Hirsch, Differential Topology (Springer, N.Y., 1976; Mir Moscow, 1979).
K. Kuratowski, Topology. Vol. 1 (Academic Press, N.Y., London, Warszawa, 1966; Mir, Moscow, 1966).
V. M. Millionshchikov, “Unsolved Problem on Central Exponents,” Differ. Uravn. 24 (12), 2184 (1988).
V. M. Millionshchikov, “On Baire Class of Central Exponents,” Differ. Uravn. 25 (12), 2190 (1989).
V. M. Millionshchikov, “Relative Bohl Exponents and Baire Classes of Functions,” Differ. Uravn. 26 (6), 1087 (1990).
V. V. Bykov, “Bohl Exponents and Baire Classes of Functions,” in: Trudy Semin. I. G. Petrovskogo, Vol 30 (Moscow State Univ., Moscow, 2014), pp. 94–121.
J. Dugundji, Topology (Allyn and Bacon, Boston, 1966).
K. Kuratowski, Topology. Vol. 2 (Academic Press, N.Y., London, Warszawa, 1968; Mir, Moscow, 1969).
V. M. Millionshchikov, “Lyapunov Exponents as Functions of Parameter,” Matem. Sborn. 137 (3), 364 (1988).
F. Hausdorff, Set Theory (von Veit, Leipzig, 1914; ONTI, Moscow, 1937).
Author information
Authors and Affiliations
Corresponding author
Additional information
Russian Text © The Author(s), 2019, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2019, Vol. 74, No. 5, pp. 17–22.
About this article
Cite this article
Bykov, V.V. To Millionshchikov’s Problem on the Baire Class of Central Exponents of Diffeomorphisms. Moscow Univ. Math. Bull. 74, 189–194 (2019). https://doi.org/10.3103/S0027132219050036
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0027132219050036