Abstract
In a one-parameter family of quadratic maps of a plane we indicate an interval of parameter values such that every map with a parameter value in the indicated interval is a singular Morse-Smale endomorphism.
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References
D. Damanik and A. Gorodetski, “Hyperbolicity of the Trace Map for the Weakly Coupled Fibonacci Hamiltonian,” Nonlinearity 22, 123–143 (2009).
D. Damanik and A. Gorodetski, “The Spectrum of the Weakly Coupled Fibbonacci Hamiltonian,” Elect. Research Announcements, Math. Sci. 16, 23–29 (2009).
Y. Avishai and D. Berend, “Transmission Through a One-Dimensional Fibonacci Sequence of δ-Function Potentials,” Physical Review B 41(9), 5492–5499 (1990).
Y. Avishai, D. Berend, and V. Tkachenko, “Trace Maps,” Int. J. Modern Physics B 11(30), 3525–3542 (1997).
A. N. Sharkovskii, “Problem List,” in Proceedings of International Conference “Low Dimensional Dynamics”, Oberwolfach, Germany, April 25–May 1 1993 (Tagungsbericht 20, 1993), p. 17.
S. S. Bel’mesova and L. S. Efremova, “Quadratic Maps of Some One-Parameter Family which are Close to the Unperturbed One,” Trudy MFTI, No. 2 (2), 46–57 (2010).
S. S. Bel’mesova and L. S. Efremova, “Invariant Sets of Some Quadratic Maps of the Plane,” Vestnik Nizhegorodskogo Univ. Ser. Matem., No. 2 (2), 152–158 (2012).
A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems (Factorial, Moscow, 1999) [Russian translation].
M. Brin and Ya. Pesin, “On Morse-Smale Endomorphisms,” American Math. Soc. Transl. 171(2), 35–45 (1996).
D. Azimov, “Round Handles and Non-Singular Morse-Smale Flows,” Ann.Math. 102, 41–54 (1975).
A. N. Sharkovskii, Yu. L. Maistrenko, and E. Yu. Romanenko, Difference Equations and Their Applications (Nauk. Dumka, Kiev, 1986) [in Ukrainian].
J. Marsden and M. McCracken, The Hopf Bifurcation and its Applications (Mir, Moscow, 1980) [Russian translation].
A. A. Andronov, E. A. Leontovich, I. I. Gordon and A. G. Maier, Qualitative Theory of Second-Order Dynamic Systems (Nauka, Moscow, 1966) [in Russian].
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Original Russian Text © S.S. Bel’mesova and L.S. Efremova, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 8, pp. 80–85.
Submitted by A.M. Bikchentaev
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Bel’mesova, S.S., Efremova, L.S. A one-parameter family of quadratic maps of a plane including Morse-Smale endomorphisms. Russ Math. 57, 70–74 (2013). https://doi.org/10.3103/S1066369X13080082
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DOI: https://doi.org/10.3103/S1066369X13080082