Perturbation of a stable invariant torus of a dynamical system

1972 ◽  
Vol 23 (1) ◽  
pp. 117-123 ◽  
Author(s):  
V. L. Golets
Keyword(s):  
Dynamical System ◽  
Invariant Torus ◽  
Stable Invariant ◽  
Stable Invariant Torus

scholarly journals On preservation of an exponentially stable invariant torus

2015 ◽  
Vol 63 (1) ◽  
pp. 215-222 ◽  
Author(s):  
Mykola Perestyuk ◽  
Petro Feketa
Keyword(s):  
Simple Structure ◽  
Linear Extensions ◽  
Qualitative Behaviour ◽  
Small Perturbations ◽  
One Dimensional ◽  
Exponentially Stable ◽  
Invariant Toroidal Manifold ◽  
Dimensional Dynamical System ◽  
Stable Invariant ◽  
Stable Invariant Torus

Abstract New conditions of the preservation of an exponentially stable invariant toroidal manifold of linear extension of one-dimensional dynamical system on torus under small perturbations in ω-limit set are established. This approach is applied to the investigation of the qualitative behaviour of solutions of linear extensions of dynamical systems with simple structure of limit sets.

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