References
Yudovich V. I., “Cosymmetry and oscillation instability. I. Branching of a limit cycle from a continuous family of equilibria in a dynamical system with cosymmetry,” submitted to VINITI on October 28, 1994, No. 2440-B94.
Yudovich V. I., “Cosymmetry and oscillation instability. II. An example of delaying the bifurcation of the branching of a cycle. Study of stability of a limit cycle,” submitted to VINITI on November 30, 1995, No. 3187-B95.
Yudovich V. I., “On the bifurcation of the branching of a cycle from a family of equilibria of a dynamical system and its delaying,” Prikl. Mat. i. Mekh.,62, No. 1, 22–34 (1998).
Kurakin L. G. andYudovich V. I., “Bifurcation of the branching of a cycle in a system with cosymmetry,” Dokl. Akad. Nauk,358, No. 3, 346–349 (1998).
Kurakin L. G. andYudovich V. I., “Bifurcation of the branching of a cycle inn-parameter family of dynamic system with cosymmetry,” Chaos,7, No. 3, 376–386 (1997).
Kurakin L. G. andYudovich V. I., “On auto-oscillation regimes in systems with cosymmetry,” in: Modern Problems of Continuum Mechanics (Proceedings of the International Conference, Rostov-on-Don, September 19–20, 1996) [in Russian], Kniga, Rostov-on-Don, 1996,3, pp. 99–103.
Yudovich V. I., “Cosymmetry, degeneration of solutions of operator equations, and origination of a filtration convection,” Mat. Zametki,49, No. 5, 142–148 (1991).
Yudovich V. I., “An implicit function theorem for cosymmetric equations,” Mat. Zametki,60, No. 2, 313–317 (1996).
Yudovich V. I., “The cosymmetric version of implicit function theorem,” in: Linear Topological Spaces and Complex Analysis, Middle East Techn. Univ., Ankara, 1995,2, pp. 105–125.
Yudovich V. I., “Secondary cycle of equilibria in a system with cosymmetry, its creation by bifurcation and impossibility of symmetric treatment of it,” Chaos,5, No. 2, 402–411 (1995).
Kurakin L. G., “Critical cases of stability. Conversion of the implicit function theorem for dynamical systems with cosymmetry,” Mat. Zametki,63, No. 4, 572–578 (1998).
Marsden J. E. andMcCracken M. The Hopf Bifurcation and Its Applications [Russian translation], Mir, Moscow (1980).
Kurakin L. G. and Yudovich V. I., “Bifurcation of the branching of a cycle in a dynamical system with cosymmetry,” submitted to VINITI on January 20, 1998, No. 150-B98.
Amiton, A. D., “A model of a dynamical system with two cosymmetries,” submitted to VINITI on February 17, 1998, No. 465-B98.
Govorukhin V. N., “Numerical study of stability failure for derived steady regimes in the Darcy plane convection problem,” Dokl. Akad. Nauk,363, No. 6, 772–774 (1998).
Yudovich V. I., “Cosymmetry and dynamical systems,” Proc. ICIAM Ser. Applied Sciences, Especially Mechanics, No. 4, 585–588 (1995).
Daletskiî, Yu. L. andKreîn M. G., Stability of Solutions to Differential Equations in Banach Space [in Russian], Nauka, Moscow (1970).
Yudovich V. I., The Linearization Method in Hydrodynamical Stability Theory [in Russian, (English. transl.: V. I. Yudovich, The Linearization Method in Hydrodynamical Stability Theory, Transl. of Math. Monographs,4, AMS, Providence (1989))], Rostovsk. Univ., Rostov-on-Don (1984).
Kreîn S. G., Linear Differential Equations in Banach Space [in Russian], Nauka, Moscow (1967).
Yudovich V. I., “Origination of auto-oscillations in a fluid,” Prikl. Mat. i Mekh.,35, No. 4, 638–655 (1971).
Additional information
The research was supported by the Russian Foundation for Basic Research (Grant 96-01-01791), the Competition Center for Basic Natural Sciences at St. Petersburg State University (Gratn 95-0-2.1-115) and the International Interinstitutional Program “Russian Universities”–Basic Research (Gratn 4087).
Rostov-on-Don. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 41, No. 1, pp. 136–149, January–February, 2000.
Rights and permissions
About this article
Cite this article
Kurakin, L.G., Yudovich, V.I. Application of the Lyapunov-Schmidt method to the problem of the branching of a cycle from a family of equilibria in a system with multicosymmetry. Sib Math J 41, 114–124 (2000). https://doi.org/10.1007/BF02674001
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02674001