Perturbations of Systems Describing the Motion of a Particle in Central Fields

Christov, Ognyan; Dragnev, Dragomir

Displaying similar documents to “Perturbations of Systems Describing the Motion of a Particle in Central Fields”

On the KAM - Theory Conditions for the Kirchhoff Top

Christov, Ognyan (1997)

Serdica Mathematical Journal

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* Partially supported by Grant MM523/95 with Ministry of Science and Technologies. In this paper the classical Kirchhoff case of motion of a rigid body in an infinite ideal fluid is considered. Then for the corresponding Hamiltonian system on the zero integral level, the KAM theory conditions are checked. In contrast to the known similar results, there exists a curve in the bifurcation diagram along which the Kolmogorov’s condition vanishes for certain values of the parameters. ...

On the Isoenergetical Non-Degeneracy of the Problem of two Centers of Gravitation

Dragnev, Dragomir (1997)

Serdica Mathematical Journal

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* Partialy supported by contract MM 523/95 with Ministry of Science and Technologies of Republic of Bulgaria. For the system describing the motion of a moss point under the action of two static gravity centers (with equal masses), we find a subset of the set of the regular values of the energy and momentum, where the condition of isoenergetical non-degeneracy is fulfilled.

Perturbations of quadratic hamiltonian systems with symmetry

Emil Ivanov Horozov, Iliya Dimov Iliev (1996)

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Classical integrable mechanical systems and their integrable perturbations.

Dragović, Vladimir (1998)

Publications de l'Institut Mathématique. Nouvelle Série

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Chaotic behaviour in the solar system

Stefano Marmi (1998-1999)

Séminaire Bourbaki

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Multidimensional two-particles problem with non-central potential

D. V. Choodnovsky, G. V. Choodnovsky (1977-1978)

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Rigorous results on the power expansions for the integrals of a hamiltonian system near an elliptic equilibrium point

Antonio Giorgilli (1988)

Annales de l'I.H.P. Physique théorique

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Limit Cycles of Perturbations of a Class of Quadratic Hamiltonian Vector Fields

Markov, Yavor (1996)

Serdica Mathematical Journal

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We prove that in quadratic perturbations of generic Hamiltonian vector fields with two saddle points and one center there can appear at most two limit cycles. This bound is exact.

A new hierarchy of integrable system of $1 + 2$ dimensions: from Newton's law to generalized Hamiltonian system. II.

Huang, Xuncheng, Tu, Guizhang (2006)

International Journal of Mathematics and Mathematical Sciences

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A simple proof of the non-integrability of the first and the second Painlevé equations

Henryk Żołądek (2011)

Banach Center Publications

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The first and the second Painlevé equations are explicitly Hamiltonian with time dependent Hamilton function. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems in ℂ⁴. We prove that the latter systems do not have any additional algebraic first integral. In the proof equations in variations with respect to a parameter are used.