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| Topological analysis of a completely integrable system supposes a description of the topological structure of all regular integral manifolds and critical integral surfaces and a possibility to find out the bifurcations occurring along any path in the phase space. Having a system with non-linear first integrals, we present an approach to calculate explicitly all bifurcations called the method of critical subsystems. We also describe a general way of the most compact description of the topology of an integrable system in the form of the topological atlas of the system. To build topological atlases one can use contemporary computer algebra programs. We present an electronic realization of such an atlas for one of the most topologically complicated systems in the dynamics of a gyrostat with a fixed point generalizing the classical Kowalevski problem. |
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