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A criterion for the existence of the unique invariant torus of a linear extension of dynamical systems

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Abstract

Under the assumption that a linear homogeneous system defined on the direct product of a torus and the Euclidean space is exponentially dichotomous on semiaxes, we obtain a necessary and sufficient condition for the existence of the unique invariant torus of the corresponding inhomogeneous linear system.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    A. A. Boichuk

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  1. A. A. Boichuk
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 1, pp. 3–13, January, 2007.

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Boichuk, A.A. A criterion for the existence of the unique invariant torus of a linear extension of dynamical systems. Ukr Math J 59, 1–11 (2007). https://doi.org/10.1007/s11253-007-0001-8

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  • DOI: https://doi.org/10.1007/s11253-007-0001-8

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