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Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 6, Pages 1259–1274 (Mi izv2361)  

This article is cited in 28 scientific papers (total in 29 papers)

On an additive functional homology equation connected with an ergodic rotation of the circle

D. V. Anosov

Abstract: It is shown that the title equation with continuous and even analytic right-hand side may have a measurable solution which is not Lebesgue integrable (and even with “worse” properties).

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English version:
Mathematics of the USSR-Izvestiya, 1973, 7:6, 1257–1271

Bibliographic databases:

UDC: 517.9
MSC: Primary 28A65; Secondary 39A15
Received: 14.02.1973

Citation: D. V. Anosov, “On an additive functional homology equation connected with an ergodic rotation of the circle”, Izv. Akad. Nauk SSSR Ser. Mat., 37:6 (1973), 1259–1274; Math. USSR-Izv., 7:6 (1973), 1257–1271

Citation in format AMSBIB
\by D.~V.~Anosov
\paper On an additive functional homology equation connected with an ergodic rotation of the circle
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1973
\vol 37
\issue 6
\pages 1259--1274
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 6
\pages 1257--1271

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    This publication is cited in the following articles:
    1. A. B. Krygin, “On $\omega$-limit sets of a cylindrical cascade”, Math. USSR-Izv., 9:4 (1975), 831–849  mathnet  crossref  mathscinet  zmath
    2. A. Ya. Gordon, “Sufficient condition for unsolvability of the additive functional homological equation connected with the ergodic rotation of a circle”, Funct. Anal. Appl., 9:4 (1975), 334–336  mathnet  crossref  mathscinet  zmath
    3. I. P. Kornfeld, “Algebraic curves and commuting matricial differential operators”, Funct. Anal. Appl., 10:2 (1976), 143–144  mathnet  crossref  mathscinet  zmath
    4. Michael Robert Herman, “Sur la Conjugaison Différentiable des Difféomorphismes du Cercle a des Rotations”, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, 49:1 (1979), 5  crossref  mathscinet  zmath
    5. E. A. Sidorov, “Conditions for uniform Poisson stability of cylindrical systems”, Russian Math. Surveys, 34:6 (1979), 220–224  mathnet  crossref  mathscinet  zmath
    6. Yu. D. Latushkin, “On integro-functional operators with a shift which is not one-to-one”, Math. USSR-Izv., 19:3 (1982), 479–493  mathnet  crossref  mathscinet  zmath
    7. Yu. D. Latushkin, A. M. Stepin, “Weighted shift operator, spectral theory of linear extensions, and the Multiplicative Ergodic Theorem”, Math. USSR-Sb., 70:1 (1991), 143–163  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. Yu. D. Latushkin, A. M. Stepin, “Weighted translation operators and linear extensions of dynamical systems”, Russian Math. Surveys, 46:2 (1991), 95–165  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. A. V. Rozhdestvenskii, “On the coboundedness of functions on a torus”, Math. Notes, 55:6 (1994), 617–622  mathnet  crossref  mathscinet  zmath  isi
    10. V. V. Ryzhikov, “The absence of mixing in special flows over rearrangements of segments”, Math. Notes, 55:6 (1994), 648–650  mathnet  crossref  mathscinet  zmath  isi
    11. A. V. Rozhdestvenskii, “K neravenstvu Dzheksona v $L_p(\mathbb T^d)$”, Fundament. i prikl. matem., 1:3 (1995), 753–766  mathnet  mathscinet  zmath
    12. V. I. Arnol'd, A. A. Bolibrukh, R. V. Gamkrelidze, V. P. Maslov, E. F. Mishchenko, S. P. Novikov, Yu. S. Osipov, Ya. G. Sinai, A. M. Stepin, L. D. Faddeev, “Dmitrii Viktorovich Anosov (on his 60th birthday)”, Russian Math. Surveys, 52:2 (1997), 437–445  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    13. A. V. Kochergin, “A mixing special flow over a circle rotation with almost Lipschitz function”, Sb. Math., 193:3 (2002), 359–385  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. A. V. Rozhdestvenskii, “On absolutely continuous weakly mixing cocycles over irrational rotations”, Sb. Math., 194:5 (2003), 775–792  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    15. A. V. Kochergin, “Hölder Time Change and Mixing Rate in a Flow on the Two-Dimensional Torus”, Proc. Steklov Inst. Math., 244 (2004), 201–232  mathnet  mathscinet  zmath
    16. A. V. Rozhdestvenskii, “On the additive cohomological equation and time change for a linear flow on the torus with a Diophantine frequency vector”, Sb. Math., 195:5 (2004), 723–764  mathnet  crossref  crossref  mathscinet  zmath  isi
    17. A. B. Antonevich, “Coherent Local Hyperbolicity of a Linear Extension and the Essential Spectra of a Weighted Shift Operator on a Closed Interval”, Funct. Anal. Appl., 39:1 (2005), 9–20  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    18. L. S. Efremova, “On the nonwandering set and center of some skew products of mappings of the interval”, Russian Math. (Iz. VUZ), 50:10 (2006), 17–25  mathnet  mathscinet  elib
    19. V. V. Kozlov, “Dynamical Systems with Multivalued Integrals on a Torus”, Proc. Steklov Inst. Math., 256 (2007), 188–205  mathnet  crossref  mathscinet  zmath  elib  elib
    20. A. V. Kochergin, “Nondegenerate Saddle Points and the Absence of Mixing in Flows on Surfaces”, Proc. Steklov Inst. Math., 256 (2007), 238–252  mathnet  crossref  mathscinet  zmath  elib  elib
    21. A. V. Rozhdestvenskii, “An Additive Cohomological Equation and Typical Behavior of Birkhoff Sums over a Translation of the Multidimensional Torus”, Proc. Steklov Inst. Math., 256 (2007), 263–274  mathnet  crossref  mathscinet  zmath  elib  elib
    22. A. V. Rozhdestvenskii, “On non-trivial additive cocycles on the torus”, Sb. Math., 199:2 (2008), 229–251  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    23. Filchenkov A.S., “Primer topologicheski tranzitivnogo, no ne topologicheski ergodicheskogo gladkogo kosogo proizvedeniya na ploskosti”, Vestnik nizhegorodskogo universiteta im. N.I. Lobachevskogo, 2012, 193–201  elib
    24. Efremova L.S., Filchenkov A.S., “Topologicheskaya tranzitivnost kosykh pro- izvedenii v ploskosti s otritsatelnym shvartsianom semeistva otobrazhenii v sloyakh”, Trudy moskovskogo fiziko-tekhnicheskogo instituta, 2012, 82–93  elib
    25. L. S. Efremova, “A decomposition theorem for the space of $C^1$-smooth skew products with complicated dynamics of the quotient map”, Sb. Math., 204:11 (2013), 1598–1623  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    26. Teube S. Mbainaisem, Serin A. Lo, Mussa O. A. Salem, “O privodimosti operatorov vzveshennoi kompozitsii”, PFMT, 2015, no. 2(23), 75–82  mathnet
    27. V. V. Kozlov, “Invariant measures of smooth dynamical systems, generalized functions and summation methods”, Izv. Math., 80:2 (2016), 342–358  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    28. L. S. Efremova, “Dynamics of skew products of interval maps”, Russian Math. Surveys, 72:1 (2017), 101–178  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    29. A. V. Kochergin, “New examples of Besicovitch transitive cylindrical cascades”, Sb. Math., 209:9 (2018), 1257–1272  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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