We obtain exact formulas describing the nonwandering set of a C 1-smooth skew product of interval maps with Ω-stable quotient map of type ≻ 2∞.
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A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, Cambridge (1997).
L. S. Efremova, “Nonwandering set and center of triangular maps with a closed set of periodic points in base” [in Russian], In: Dynamical Systems and Nonlinear Phenomena pp. 15–25, Kiev (1990).
L. S. Efremova, “Nonwandering set and center of some skew products of interval maps” [in Russian], Izv. Vyssh. Uchebn. Zaved., Mat. No. 10, 19-28 (2006); English transl.: Rus. Math. 50, No. 10, 17-25 (2006).
J. L. G. Guirao and F. L. Pelao, “On skew product maps with the base having a closed set of periodic points,” Intern. J. Comput. Math. 83, 441-445 (2008).
J. L. G. Guirao and R. G. Rubio, “Nonwandering set of skew product maps with base having closed set of periodic points,” J. Math. Anal. Appl. 362, 350-354 (2010).
L. S. Efremova, “Remarks on the nonwandering set of skew products with a closed set of periodic points of the quotient map,” Springer Proc. Math. Stat. 57, 39-58 (2014).
J. Kupka, “The triangular maps with closed sets of periodic points,” J. Math. Anal. Appl. 319, 302–314 (2006).
C. Arteaga, “Smooth Triangular Maps of the Square with Closed Set of Periodic Points,” J. Math. Anal. Appl. 196, 987–997 (1995).
K. Kuratowski, Topology. I. II, Academic Press, New York etc. (1966), (1968),
M. V. Jakobson, “On smooth mappings of the circle into itself” [in Russian] Mat. Sb. 85, No. 2, 163-188 (1971); English transl.: Math. USSR Sb. 14, No. 2, 161-185 (1971).
L. S. Efremova, “On the concept of Ω-function for the skew products of interval mappings” [in Russian], Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh. Temat. Obz. 67, 129-160 (1999); English transl.: J. Math. Sci., New York 105, No. 1, 1779-1798 (2001).
L. S. Efremova, “Space of C 1-smooth skew products of maps of an interval” [in Russian], Teor. Mat. Fiz. 164, No. 3, 447-454 (2010); English transl.: Theor. Math. Phys. 164 (3), 1208-1214 (2010).
L. S. Efremova, “A decomposition theorem for the space of C 1-smooth skew products with complicated dynamics of quotient maps” [in Russian], Mat. Sb. 204, No. 11, 55-82 (2013); English transl.: Sb. Math. 204 (11), 1598-1623 (2013).
L. S. Efremova, “Multivalued functions and nonwandering set of skew products of maps of an interval with complicated dynamics of quotient map” [in Russian], Izv. Vyssh. Uchebn. Zaved., Mat. No. 2, 93-98 (2016); English transl.: Rus. Math. 60, No. 2, 77-81 (2016).
E. M. Coven and Z. Nitecki, “Nonwandering sets of the powers of maps of the interval,” Ergod. Theor. Dynam. Syst. 1, 9-31 (1981).
Z. Nitecki, “Topological dynamics on the interval,” Prog. Math. 21, 1-73 (1982).
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Translated from Problemy Matematicheskogo Analiza 85, June 2016, pp. 83-94.
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Efremova, L.S. Nonwandering Sets of C 1-Smooth Skew Products of Interval Maps with Complicated Dynamics of Quotient Map. J Math Sci 219, 86–98 (2016). https://doi.org/10.1007/s10958-016-3085-6
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DOI: https://doi.org/10.1007/s10958-016-3085-6