一类非游荡算子的小扰动下的不变性

Invariance of one class of nonwandering operator under small perturbation

对于一种新型的线性混沌算子——非游荡算子,研究Banach空间上的一类特殊非游荡算子——可逆线性有界非游荡算子,证明它的小扰动下的不变性.利用矩阵和不变集的方法证明在非游荡算子的一充分小的领域内,非游荡算子保持它的非游荡性不变.即充分靠近非游荡线性算子的可逆线性算子是非游荡的.

For a new kind of linear chaotic operator（ nonwandering operator）, one class of nonwande-ring operators （invertible and bounded linear nonwandering operators） are studied, and their invariance under small perturbation in finite dimensional separable Banach Space is proved. It is proved that nonwandering operators keep their property of nonwandering on this small neighborhood by the methods of matrices and invariant set. That is to say, invertible and bounded linear operators which are close to the nonwandering operator enough are nonwandering operators.