References
L. S. Efremova, “Nonwandering set and center of triangular maps with closed set of periodic points in the base,” in: Dynamical Systems and Nonlinear Phenomena [in Russian], Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1990), pp. 16–25.
Z. Nitecki, Introduction to Differential Dynamics [Russian translation], Mir, Moscow (1975).
S. F. Kolyada and A. N. Sharkovsky, “On topological dynamics of triangular maps of the plane,” European Conference on Iteration Theory, Austria, Sept. 10–16, 1989.
M. V. Yakobson, “Smooth maps of a circle into itself,” Mat. Sb.,85, No. 2, 163–188 (1971).
A. N. Sharkovskii, “Cycles of a continuous map,” Ukr. Mat. Zh.,17, No. 3, 104–111 (1965).
A. N. Sharkovskii, “Attracting sets which do not contain cycles,” Ukr. Mat. Zh.,20, No. 1, 136–142 (1968).
A. N. Sharkovskii, “A map with topological entropy zero having a continuum of Cantor minimal sets,” in: Dynamical Systems and Turbulence [in Russian], Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1989), pp. 109–117.
A. N. Sharkovskii, “The problem of isomorphism of dynamical systems,” in: Proceedings of the Fifth International Conference on Nonlinear Oscillations. Vol. 2. Qualitative Methods [in Russian], Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1970), pp. 541–544.
L. Block, “Homoclinic points of mappings of the interval,” Proc. Am. Math. Soc.,72, No. 3, 576–580 (1978).
A. N. Sharkovskii, “Descriptive estimates of the set of homoclinic points of a dynamical system,” in: Differential-Difference Equations and Problems of Mathematical Physics [in Russian], Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1984), pp. 109–115.
E. P. Kloeden, “On Sharkovsky's cycle coexistence ordering,” Bull. Austral. Math. Soc.,20, 171–177 (1979).
A. N. Sharkovskii, “Problems of the theory of ordinary differential equations,” Usp. Mat. Nauk,38, No. 5, 172 (1983).
L. S. Efremova, “Fibered dynamical systems with nonempty set of periodic points,” in: Seventh All-Union Conference on the Qualitative Theory of Differential Equations. Riga, April 3–7, 1989 [in Russian], Riga (1989), p. 92.14.
K. Kuratowsky, Topology [Russian translation], Vol. 1, Mir, Moscow (1966).
D. V. Anosov, “A class of invariant sets of smooth dynamical systems,” in: Proceedings of the Fifth International Conference on Nonlinear Oscillations. Vol. 2: Qualitative Methods [in Russian], Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1970), pp. 39–45.
L. Block and J. E. Franke, “The chain recurrent set, attractors, explosions,” Ergod. Theory Dynam. Syst.,5, 321–327 (1985).
A. N. Sharkovsky, “How complicated can be one dimensional systems: descriptive estimates of sets,” in: Dyn. Syst. Ergod. Theory. Banach Centre Publ.; PWN, Vol. 23, Warszawa (1989), pp. 447–453.
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Translated from Matematicheskie Zametki, Vol. 54, No. 3, pp. 18–33, September, 1993.
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Efremova, L.S. A class of twisted products of maps of an interval. Math Notes 54, 890–898 (1993). https://doi.org/10.1007/BF01209553
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DOI: https://doi.org/10.1007/BF01209553