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Frontiers and symmetries of dynamical systems

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2010
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Taylor & Francis
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The frontiers of boundedness F(b) of the orbits of dynamical systems X defined on R(n) are studied. When X is completely integrable some topological properties of F(b) are found and, in certain cases, F(b) is localized with the help of symmetries of X. Several examples in dimensions 2 and 3 are provided. In case the number of known first integrals of the vector field X is less than n - 1, an interesting connection of F(b) with the frontier of boundedness of the level-sets of the first integrals of X is proved. This result also applies to Hamiltonian systems.
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