DYNAMICS OF A HAMILTONIAN SYSTEM WITH FOUR DEGREES OF FREEDOM

Svetoslav Nikolov; Vassil Zlatanov

Scientific paper ID 1840 : 2019/3

DYNAMICS OF A HAMILTONIAN SYSTEM WITH FOUR DEGREES OF FREEDOM

Svetoslav Nikolov, Vassil Zlatanov

Recently, there has been an increasing interest in high-dimensional autonomous Hamiltonian systems. In this paper, we investigate the dynamics of a Hamiltonian system with four degrees of freedom. Based on our qualitative analysis, we obtain that this system has a whole plane of unstable fixed points and therefore the occurrence of chaotic behaviour is possible.

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хамилтонова система нелинейност неинтегруемост хаосHamiltonian system nonlinearity nonintegrability chaosSvetoslav Nikolov Vassil Zlatanov

BIBLIOGRAPHY

[1] Arnold, V., Kozlov, V., Neishtadt, A., Mathematical aspects of classical and celestial mechanics, 3rd. edition, Springer, NY, 2006.

[2] Skokos, Ch., On the stability of periodic orbits of high dimensional autonomous Hamiltonian systems, Physica D, vol. 159, pp. 155-179, 2001.

[3] Bountis, T., Skokos, H., Complex Hamiltonian dynamics, Springer, NY, 2012.

[4] Nikolov, S., Zaharieva, D., Dynamical behaviour of compound elastic pendulum, MATEC Web of Conferences, vol. 145, art. No 01003, 10 pages, 2018.

[5] Arnold, V., Mathematical methods of classical mechanics. Springer-Verlag, NY, 1978.

[6] Vilasi, G., Hamiltonian dynamics. World Scientific, Singapore, 2001.

[7] Wiggins, S., Global bifurcations and chaos. Analytical methods. Springer-Verlag, NY, 1988.

[8] Arrosmith, D., Place, C., Dynamical systems. Differential equations, maps and chaotic behaviour. Chapman & Hall, London, 1992.

[9] Nikolov, S., Estimating of bifurcations and chaotic behaviour in a four-dimensional system, J. of the Calcutta Math. Society, vol. 2, No 1, pp. 17-28, 2006.

[10] Ovsyannikov, I., Shilnikov, L., On systems with a saddle-focus homoclinic curve, Math. Sbornik, vol. 130(172), No 4(8), pp. 552-570, 1986.

[11] Harterich, J., Cascades of reversible homoclinic orbits to a saddle-focus equilibrium, Physica D: Nonlinear Phenomena, vol. 112, No 1-2, pp. 187-200, 1998.