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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 9 > No. 5


Product Recurrence for Weighted Backward Shifts

PP: 2361-2365
Víctor J. Galán, Félix Martínez-Giménez, Piotr Oprocha, Alfred Peris,
We study product recurrence properties for weighted backward shifts on sequence spaces. The backward shifts that have non-zero product recurrent points are characterized as Devaney chaotic shifts. We also give an example of weighted shift that admits points which are recurrent and distal, but not product recurrent, in contrast with the dynamics on compact sets. An example of a product recurrent point with unbounded orbit is also provided.

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