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Existence of an Invariant Torus for a Degenerate Linear Extension of Dynamical Systems

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Under the assumptions that a degenerate system defined on the direct product of a torus and a Euclidean space can be reduced to a central canonical form and that the corresponding homogeneous nondegenerate system is exponentially dichotomous on the semiaxes, we establish a necessary and sufficient condition for the existence of a unique invariant torus of the degenerate linear system. We also establish conditions for the preservation of an asymptotically stable invariant toroidal manifold for a degenerate linear extension of the dynamical system on a torus under small perturbations in the set of nonwandering points.

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Authors and Affiliations

  1. Uzhhorod National University, Universytets’ka Str., 14, Uzhhorod, 88000, Ukraine

    Yu. Yu. Korol’

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  1. Yu. Yu. Korol’
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Correspondence to Yu. Yu. Korol’.

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Translated from Neliniini Kolyvannya, Vol. 19, No. 2, pp. 217–226, April–June, 2016.

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Korol’, Y.Y. Existence of an Invariant Torus for a Degenerate Linear Extension of Dynamical Systems. J Math Sci 223, 273–284 (2017). https://doi.org/10.1007/s10958-017-3353-0

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  • DOI: https://doi.org/10.1007/s10958-017-3353-0

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