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On unbounded trajectories of a certain quadratic mapping of the plane

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Unbounded trajectories of the mapping F(x, y) = (xy, (x-2)2) are studied.

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References

  1. Y. Avishai and D. Berend, “Transmission through a one-dimensional Fibonacci sequence of σ-function potentials,” Phys. Rev. B., 41, No. 9, 5492–5499 (1990).

    Article  MathSciNet  Google Scholar 

  2. S. S. Bel'mesova, “On unbounded trajectories of a certain quadratic mapping of the plane,” in: III International Conference in Differential Equations and Dynamical Systems, Suzdal', Russia, July 9–14, 2006. Abstracts of Reports [in Russian], Suzdal' (2006), pp. 40–41.

  3. S. S. Belmesova, L. S. Efremova, and V. Zh. Sakbaev, “On one quadratic mapping of the plane associated with the Schrödinger equation,” in: Intern. Conf. and Workshop “Function Spaces, Approximation Theory, Nonlinear Analysis” Dedicated to the Centennial of S. M. Nikolskii, Moscow, Russia, May 23–29, 2005. Abstracts [in Russian] (2005), pp. 262.

  4. K. Bjerklöv, “Positive Lyapunov exponent and minimality for a class of one-dimensional quasi-periodic Schrödinger equation,” Ergodic Theory Dynam. Syst., 25, 1015–1045 (2005).

    Article  MATH  Google Scholar 

  5. L. Block, “Homoclinic points of mappings of the interval,” Proc. Am. Math. Soc., 72, No. 3, 576–580 (1978).

    Article  MATH  MathSciNet  Google Scholar 

  6. S. Friedland and J. Milnor, “Dynamical properties of plane polynomial automorphisms,” Ergodic Theory Dynam. Syst., 9, 67–99 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  7. S. V. Gonchenko, J. D. Meiss, and I. I. Ovsyannikov, “Chaotic dynamics of three-dimentional Henon maps that originate from a homoclinic bifurcation,” Regul. Chaotic Dyn., 11, No. 2, 191–212 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  8. M. Henon, “Numerical study of quadratic area preserving mapping,” Quart. Appl. Math., 27, 291–312 (1969).

    MATH  MathSciNet  Google Scholar 

  9. M.-C. Li and M. Malkin, “Bounded nonwandering sets for polynomial mappings,” J. Dynam. Control Syst., 10, No. 3, 377–389 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  10. “Mathematisches Forschungsinstitut Oberwolfach. Tagungsbericht 20/1993,” in: Low Dimensional Dynamics, 25.04.-1.05.1993. Problem list, pp. 17.

  11. J. Milnor and W. Thurston, “On iterated maps of the interval,” in: Dynamical Systems. College Park. 1986–1987; Lect. Notes Math., 1342, 465–563 (1988).

  12. C. Mira, L. Gardini, A. Barugola, J.-C. Cathala, “Chaotic dynamics in two-dimensional noninvertible maps,” World Sci. Ser. Nonlinear Sci. Ser. A. Monogr. Treatises, 20, 607 (1996).

    MathSciNet  Google Scholar 

  13. A. N. Sharkovskii, “On the isomorphism problem of dynamical systems,” in: Proceedings of V International Conference in Nonlinear Oscillation, Vol. 2: Qualitative methods [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1970), pp. 541–545.

    Google Scholar 

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Authors and Affiliations

  1. Nizhii Novgorod State University, Nizhii Novgorod, Russia

    S. S. Bel’mesova & L. S. Efremova

Authors
  1. S. S. Bel’mesova
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  2. L. S. Efremova
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Correspondence to L. S. Efremova.

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 53, Suzdal Conference-2006, Part 1, 2008.

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Bel’mesova, S.S., Efremova, L.S. On unbounded trajectories of a certain quadratic mapping of the plane. J Math Sci 157, 433–441 (2009). https://doi.org/10.1007/s10958-009-9324-3

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