Farhod Asrorov, Yuriy Perestyuk and Petro Feketa

On the Stability of Invariant Tori of a Class of Dynamical Systems with the Lappo-Danilevskii Condition

abstract:
The sufficient conditions for the existence of an asymptotically stable invariant toroidal manifolds of linear extensions of dynamical system on torus are obtained in the case where the matrix of the system commutes with its integral. New theorem requires the conditions to hold only in a nonwandering set of the corresponding dynamical system in order to guarantee the existence and stability of the invariant manifold. Additionally, the proposed approach is applied to the investigation of invariant sets of a certain class of discontinuous dynamical systems.

Mathematics Subject Classification: 34D35

Key words and phrases: Invariant torus, nonwandering set, Lappo-Danilevskii condition, discontinuous dynamical systems