ناوردای توپولوژیکی یک سیستم هامیلتونی انتگرال‌پذیر روی مخروط واقع در یک میدان پتانسیلی

در این مقاله توپولوژی رویه‌های هم‌انرژی غیرتکین برای سیستم هامیلتونی با دو درجۀ آزادی روی مخروط واقع در یک میدان پتانسیلی توصیف شده است. هم‌چنین روش یافتن ناوردای توپولوژیکی سیستم‌های هامیلتونی انتگرال‌پذیر از حالت فشرده به رویه‌های دوار نافشرده توسیع داده شده است.

Topological Invariant of Integrable Hamiltonian System on Cone Located in a Potential Field

The theory of topological classification of integrable Hamiltonian systems with two degrees of freedom due to Fomenko and his school . On the basis of this theory we give a topological Liouville classification of the integrable Hamiltonian systems with two degrees of freedom . Essentially , to an integrable system with two degrees of freedom which is restricted to a nonsingular 3dimensional isoenergy manifold. Fomenkochr('39')s theory ascribes in an effective way a certain discrete invariant which has the structure of a graph with numerical marks . This invariant , which is called the marked molecule or the FomenkoZieschang invariant , gives a full description (up to Liouville equivalence) of the Liouville foliation for the system.The topological classification of integrable Hamiltonian systems corresponding to the Liouville equivalence in potential fields on surfaces of revolution for surfaces that is diffeomorphic with 2dimensional sphere, contains a wide classes of mechanical systems that describes the motion of a particle on a 2dimensional sphere with revolution metric, which has been studied.In this paper, the topology of nonsingular isoenergy surfaces for a Hamiltonian system with two degrees of freedom on a cone located in a potential field is described. Also, the method of finding the topological invariant of integrable Hamiltonian systems is extended from compact case to noncompact rotating surfaces../files/site1/files/64/8.pdf