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References
D. V. Anosov, S. Kh. Aranson, I. U. Bronshtein, and V. Z. Grines, “Smooth dynamical systems,” in: Progress in Science and Technology, Series on Contemporary Problems in Mathematics, Fundamental Directions, Smooth Dynamical Systems-1 [in Russian], 1, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (1985), pp. 151–242.
D. V. Anosov, S. Kh. Aranson, V. Z. Grines, R. V. Plykin, E. A. Sataev, A. V. Safonov, A. N. Starkov, A. M. Stepin, and S. V. Shlyachkov, “Dynamical systems with hyperbolic behavior,” in: Progress in Science and Technology, Series on Contemporary Problems in Mathematics, Fundamental Directions, Smooth Dynamical Systems-9 [in Russian], 66, All-Union Institute for Scientific and Technical Information, USSR Academy of Sciences, Moscow (1991), pp. 151–242.
J. Birkhoff, Dynamical Systems [Russian translation], Gostekhizdat, Moscow (1941).
L. S. Efremova, Periodic Motions of Discrete Semidynamical Systems [in Russian], Dissertation, Gor’kii (1981).
L. S. Efremova, “On the nonwandering set and the center of triangular mappings with a closed set of periodic points in the base,” in: Dynamical Systemps and Nonlinear Phenomena [in Russian], Institute of Mathematics, Ukr. Acad. Sci., Kiev (1990), pp. 15–25.
L. S. Efremova, “On the concept of Ω-function of the skew product of interval mappings,” in: Progress in Science and Technology, Series on Contemporary Mathematics and Its Applications, Thematical Surveys [in Russian], 67, All-Russian Institute for Scientific and Technical Information, Russian Academy of Sciences, Moscow (1999), pp. 129–160.
L. S. Efremova, “New set-valued functions in the theory of skew products of interval maps,” Nonlinear Anal., 47, 5297–5308 (2001).
L. S. Efremova, “Set-valued functions and dynamics of skew products of interval maps,” in: Proc. Int. Conf. Dedicated to the 100th anniversary of A. A. Andronov, Nizhny Novgorod, July 2–6, 2001, Progr. Nonlin. Science. Math. Problems of Nonlinear Dynamics, 1, Nizhnii Novgorod (2002), pp. 219–224.
M. V. Jakobson, “On smooth self-mappings of a circle,” Mat. Sb., 85, No. 2, 163–188 (1971).
A. N. Kolmogorov and S. V. Fomin, Elements of Function Theory and Functional Analysis [in Russian], Nauka, Moscow (1972).
K. Kuratowski, Topology [Russian translation], Vol. 1, Mir, Moscow (1966).
A. G. Maier, “On a certain Birkhoff problem,” Dokl. Akad. Nauk SSSR, 55, No. 6, 477–479 (1947).
A. G. Maier, “On trajectories in the three-dimensional space,” Dokl. Akad. Nauk SSSR, 55, No. 7, 583–585 (1947).
A. G. Maier, “On the order number of central trajectories,” Dokl. Akad. Nauk SSSR, 59, No. 8, 1393–1396 (1948).
A. G. Maier, “On central trajectories and the Birkhoff problem,” Mat. Sb., 25 (1949).
V. V. Nemytskii, “Topological problems of dynamical system theory,” Usp. Mat. Nauk, 4, No. 6, 91–153 (1949).
H. Poincaré, Selected Works, Vol. 2, New Methods of Celestial Mechanics, III, Integral Invariant, Periodic Solutions of the Second Kind, Doubly-Asymptotic Solutions [Russian translation], USSR Academy of Sciences, Moscow (1972).
A. N. Sharkovskii, “On cycles and the structure of a continuous mapping,” Ukr. Mat. Zh., 17, No. 3, 104–111 (1965).
O. M. Sharkovs’kii, “On a certain theorem of J. Birkhoff,” Dop. Ukr. RSR, Ser. A, 5, 429–432 (1967).
L. P. Shil’nikov, “On a certain Poincaré-Birkhoff problem,” Mat. Sb., 74, No. 3, 378–397 (1967).
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 36, Suzdal Conference-2004, Part 2, 2005.
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Efremova, L.S. On the structure of the set of central motions for the skew product of interval mappings. J Math Sci 145, 5219–5227 (2007). https://doi.org/10.1007/s10958-007-0346-4
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DOI: https://doi.org/10.1007/s10958-007-0346-4