Geodesic
To Millionshchikov's problem on the baire class of central exponents of diffeomorphisms
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2019), pp. 17-22

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It is shown that central exponents of a local diffeomorphism of a Riemannian manifold treated as functions on the direct product of the manifold and the space of its local diffeomorphisms with $C^1$-compact-open topology belong to the fourth Baire class. 
@article{VMUMM_2019_5_a2,
     author = {V. V. Bykov},
     title = {To {Millionshchikov's} problem on the baire class of central exponents of diffeomorphisms},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {17--22},
     publisher = {mathdoc},
     number = {5},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_5_a2/}
}
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V. V. Bykov. To Millionshchikov's problem on the baire class of central exponents of diffeomorphisms. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2019), pp. 17-22. http://geodesic.mathdoc.fr/item/VMUMM_2019_5_a2/