Lower-dimensional tori in reversible systems |
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Authors: | Sevryuk M. B. |
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Affiliation: | Institute of Energy Problems of Chemical Physics, 117829, Lenin Prospect 38, Building 2, Moscow, USSR. |
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Abstract: | On a (2n+d)-dimensional manifold M consider a vector field V reversible with respect to an involution G whose fixed point manifold is of dimension n+d. It is conjectured that generically for each 0=m=n, the phase space M contains (m+d)-parameter Cantor families of m-tori invariant under both the involution G and the flow of V. To be more precise, vector fields V with this property constitute an open set in the space of all vector fields equipped with an appropriate topology. The flow of V induces on these tori quasiperiodic motions with strongly incommensurable frequencies. Extreme cases of this conjecture (d=0, m=n, m=1, m=0) have been proven. |
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