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Journal of Mathematical Sciences

, Volume 223, Issue 3, pp 273–284 | Cite as

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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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Uzhhorod National UniversityUzhhorodUkraine

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