On the stability of sheet invariant sets of two-dimensional periodic systems

On the stability of invariant sets of leaves of three-dimensional periodic systems

“…The property of the Lipschitz condition fulfillment for the mapping ϕ is proven in the same manner as in [4]. Thus, we have introduced the Lipschitz coordinates in the vicinity of the leaf ϒ.…”

“…At the same time, it is known that the property of neutral and stable subspaces to satisfy the Lipschitz condition is a very significant constraint. In [4,5], a problem of the stability of invariant sets of two dimensional periodic systems that do not have the above property was discussed. For this purpose, the notion of a leaf of a weakly hyperbolic invariant set was introduced and a coordinate system was constructed in the vicinity of an invariant set of leaves.…”

“…We note that, if k = 1, then the problem is solved using the methods set forth in [4,5]. In this work, a case of k = 2 is considered.…”

“…The existence of such c is proven in [4]. Let N(t 0 , x 0 ) ⊂ {t = t 0 } × ‫ޒ‬ 3 , (t 0 , x 0 ) ∈ K, denote a one dimensional space perpendicular to U n (t 0 , x 0 ) at the point (t 0 , x 0 ).…”