invariant toroidal manifold
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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.

Investigation of a dynamical system in a neighborhood of an invariant toroidal manifold in the general case

1994 ◽  
Vol 46 (10) ◽  
pp. 1545-1555
Author(s):  
A. M. Samoilenko ◽  
B. P. Bazhura
Keyword(s):  
Dynamical System ◽  
Toroidal Manifold ◽  
Invariant Toroidal Manifold

Behavior of solutions of nonlinear systems of difference equations in a neighborhood of an invariant toroidal manifold

1989 ◽  
Vol 41 (1) ◽  
pp. 49-56
Author(s):  
Yu. A. Mitropol'skii ◽  
D. I. Martynyuk ◽  
V. Ya. Danilov
Keyword(s):  
Nonlinear Systems ◽  
Difference Equations ◽  
Toroidal Manifold ◽  
Invariant Toroidal Manifold
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