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Scale properties of periodic motions of nonlinear conservative oscillators with the transition to chaos

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References

  1. V. S. Anishchenko, Complex Vibrations in Simple Systems [in Russian], Nauka, Moscow (1990).

    Google Scholar 

  2. M. M. Weinberg and V. A. Trenogin, Theory of the Branching of Solutions of Nonlinear Equations [Russian translation], Nauka, Moscow (1969).

    Google Scholar 

  3. V. I. Gulyaev, V. A. Bazhenov, E. A. Gotsulyak, et al., Stability of Periodic Processes in Nonlinear Mechanical Systems [in Russian], Vyshcha Shkola, Lvov (1983).

    Google Scholar 

  4. V. I. Gulyaev, A. L. Zubritskaya, and V. L. Koshkin, “Doubling of the period of vibration of a pendulum of variable length,” Prikl. Mekh.,26, No. 6, 74–80 (1990).

    Google Scholar 

  5. V. I. Gulyaev, A. L. Zubritskaya, and V. L. Koshkin, “Construction of sequences of period-multiplying bifurcations of solutions of nonlinear ordinary differential equations,” Diff. Uravneniya,25, No. 6, 929–933 (1989).

    Google Scholar 

  6. V. I. Gulyaev, A. L. Zubritskaya, and V. L. Koshkin, “Universal sequence of bifurcations doubling the period of forced vibration of a pendulum,” Prikl. Mat. Mekh.,53, No. 5, 715–720 (1990).

    Google Scholar 

  7. B. P. Demidovich, Lectures in the Mathematical Theory of Stability [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  8. A. Lichtenberg and M. Lieberman, Regular and Stochastic Dynamics [Russian translation], Mir, Moscow (1984).

    Google Scholar 

  9. E. Everhart, An Efficient Integrator of Very High Order and Accuracy with Appendix Listing of RADAU, Univ. of Denver, Denver (1974).

    Google Scholar 

  10. M. J. Feigenbaum, Universal Behavior in Nonlinear Systems, Vol. 1, Los Alamos Sci. (1980), pp. 4–27.

    Google Scholar 

  11. Maria C. de Sousa Vieira and Gemunu H. Gunaratne, “The trajectory scaling function for period doubling bifurcations in flows,” J. Statist. Phys.,58, No. 5–6, 1245–1256 (1990).

    Google Scholar 

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Authors and Affiliations

  1. Kiev Technical University of Construction and Architecture, Ukraine

    V. I. Gulyaev & T. V. Zavrazhina

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  1. V. I. Gulyaev
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  2. T. V. Zavrazhina
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Translated from Prikladnaya Mekhanika, Vol. 32, No. 1, pp. 75–81, January, 1996.

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Gulyaev, V.I., Zavrazhina, T.V. Scale properties of periodic motions of nonlinear conservative oscillators with the transition to chaos. Int Appl Mech 32, 65–70 (1996). https://doi.org/10.1007/BF02084850

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