Skip to main content
Log in

Bifurcation of cycles from equilibria of inversion-and rotation-symmetric dynamical systems

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. R. V. Birikh, G. Z. Gershuin, E. M. Zhukhovitskii, and R. N. Rudakov, “On the oscillatory instability of the plane-parallel convective motion in a vertical channel,” Prikl. Mat. Mekh.,36, No. 4, 745–748 (1972).

    Google Scholar 

  2. V. I. Yudovich, “Free convection and bifurcation,” Prikl. Mat. Mekh.,31, No. 1, 101–111 (1967).

    Google Scholar 

  3. V. G. Babskii, “On the bifurcation of solutions of the equation Δu+λu=u2 on the sphere,” Vestn. Kharkov. Univ., No. 34, 124–135 (1970).

    Google Scholar 

  4. B. V. Loginov and V. A. Trenogin, “On the utilization of group properties for the determination of multiparameter families of solutions of nonlinear equations,” Mat. Sb.,85, No. 3, 440–454 (1971).

    Google Scholar 

  5. B. V. Loginov, “On invariant solutions in bifurcation theory,” Dokl. Akad. Nauk SSSR,246, No. 5, 1048–1051 (1979).

    Google Scholar 

  6. J. E. Marsden and M. McCracken, The Hopf Bifurcation and Its Applications, Springer-Verlag, New York-Heidelberg-Berlin (1976).

    Google Scholar 

  7. G. K. Ter-Grigor'yants, “On the onset of doubly periodic convection in a horizontal layer,” Prikl. Mat. Mekh.,37, No. 1, 177–184 (1973).

    Google Scholar 

  8. K. I. Babenko, A. L. Afendikov, and S. P. Yur'ev, “On the stability and bifurcation of the Couette flow between rotating cylinders,” Preprint No. 99, M. V. Keldysh Institute for Applied Math., Academy of Sciences of USSR (1981).

  9. V. I. Yudovich, “Onset of autooscillations in a fluid,” Prikl. Mat. Mekh.,35, No. 4, 638–655 (1971).

    Google Scholar 

  10. I. V. Morshneva and V. I. Yudovic, “Onset of secondary periodic regimes in dynamical systems with inversion and translational symmetry, applied to the problem of convection in a vertical fluid layer,” Submitted VINITI June 19, 1982 (No. 3853-82).

  11. I. S. Iokhvidov, Hankel and Toeplitz Matrices and Forms, [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  12. V. I. Yudovich, “Investigation of the autooscillations of a continuum, arising at a loss of stability of a steady-state regime,” Prikl. Mat. Mekh.,36, No. 3, 450–459 (1972).

    Google Scholar 

Download references

Authors

Additional information

Rostov-on-Don. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 26, No. 1, pp. 124–133, January–February, 1985.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Morshneva, I.V., Yudovich, V.I. Bifurcation of cycles from equilibria of inversion-and rotation-symmetric dynamical systems. Sib Math J 26, 97–104 (1985). https://doi.org/10.1007/BF00968967

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00968967

Keywords

Navigation