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 Mat. Sb. (N.S.), 1973, Volume 91(133), Number 4(8), Pages 565–579 (Mi msb3327)

Functional equations and local conjugacy of mappings of class $C^\infty$

G. R. Belitskii

Abstract: Theorems are proved on conjugacy of $C^\infty$ mappings in a neighborhood of a fixed point, under the assumption of formal conjugacy. In constrast to a well-known theorem of Sternberg, we assume the existence of a linear approximation of points of the spectrum on the unit circle and at zero. We establish theorems on conjugacy in a subgroup of the group of diffeomorphisms, and give conditions for the existence of local solutions of more general functional equations. A fixed-point principle is used in the proof.
Bibliography: 14 titles.

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English version:
Mathematics of the USSR-Sbornik, 1973, 20:4, 587–602

Bibliographic databases:

UDC: 513.83+517.948
MSC: Primary 47H15, 57D50; Secondary 47H10

Citation: G. R. Belitskii, “Functional equations and local conjugacy of mappings of class $C^\infty$”, Mat. Sb. (N.S.), 91(133):4(8) (1973), 565–579; Math. USSR-Sb., 20:4 (1973), 587–602

Citation in format AMSBIB
\Bibitem{Bel73} \by G.~R.~Belitskii \paper Functional equations and local conjugacy of mappings of class~$C^\infty$ \jour Mat. Sb. (N.S.) \yr 1973 \vol 91(133) \issue 4(8) \pages 565--579 \mathnet{http://mi.mathnet.ru/msb3327} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=358852} \zmath{https://zbmath.org/?q=an:0283.39007} \transl \jour Math. USSR-Sb. \yr 1973 \vol 20 \issue 4 \pages 587--602 \crossref{https://doi.org/10.1070/SM1973v020n04ABEH002001} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. G. R. Belitskii, “Germs of mappings $\omega$-determined with respect to a given group”, Math. USSR-Sb., 23:3 (1974), 425–440
2. G. R. Belitskii, “Normal forms for formal series and germs of $C^\infty$-mappings with respect to the action of a group”, Math. USSR-Izv., 10:4 (1976), 809–821
3. L. P. Kuchko, “Linear functional equations”, Math. USSR-Izv., 12:2 (1978), 357–370
4. G. R. Belitskii, “Equivalence and normal forms of germs of smooth mappings”, Russian Math. Surveys, 33:1 (1978), 107–177
5. D. B. A. Epstein, “Commutators ofC ∞-diffeomorphisms. Appendix to “A Curious Remark Concerning the Geometric Transfer Map” by John N. Mather”, Comment Math Helv, 59:1 (1984), 111
6. G. R. Belitskii, “Sternberg's theorem for Banach spaces”, Funct. Anal. Appl., 18:3 (1984), 238–239
7. G. R. Belitskii, “Smooth equivalence of germs of vector fields with a single zero eigenvalue or a pair of purely imaginary eigenvalues”, Funct. Anal. Appl., 20:4 (1986), 253–259
8. M. Ya. Zhitomirskii, “Degeneracies of differential 1-forms and Pfaffian structures”, Russian Math. Surveys, 46:5 (1991), 53–90
9. VICTORIA RAYSKIN, “Theorem of Sternberg–Chen modulo the central manifold for Banach spaces”, Ergod Th Dynam Sys, 2009, 1
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