On Preservation of the Invariant torus for Multifrequency Systems
We establish new conditions for the preservation of an asymptotically stable invariant toroidal manifold of the linear extension of a dynamical system on a torus under small perturbations in a set of nonwandering points. The proposed approach is applied to the investigation of the existence and stab...
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| Date: | 2013 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2013
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2529 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We establish new conditions for the preservation of an asymptotically stable invariant toroidal manifold of the linear extension of a dynamical system on a torus under small perturbations in a set of nonwandering points. The proposed approach is applied to the investigation of the existence and stability of the invariant tori of linear extensions of the dynamical systems with simple structures of limit sets and recurrent trajectories. |
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