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Conservation and bifurcation of an invariant torus of a vector field

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Abstract

We consider small perturbations with respect to a small parameter ε≥0 of a smooth vector field in ℝn+m possessing an invariant torusT m. The flow on the torusT m is assumed to be quasiperiodic withm basic frequencies satisfying certain conditions of Diophantine type; the matrix Ω of the variational equation with respect to the invariant torus is assumed to be constant. We investigate the existence problem for invariant tori of different dimensions for the case in which Ω is a nonsingular matrix that can have purely imaginary eigenvalues.

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Authors and Affiliations

  1. St.-Petersburg State University, St Petersburg, USSR

    Yu. N. Bibikov

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  1. Yu. N. Bibikov
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Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 34–44, January, 1997.

Translated by S. K. Lando

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Bibikov, Y.N. Conservation and bifurcation of an invariant torus of a vector field. Math Notes 61, 29–37 (1997). https://doi.org/10.1007/BF02355005

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  • DOI: https://doi.org/10.1007/BF02355005

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