This is an announcement for the paper "Li-Yorke and distributionally chaotic operators" by T. Bermudez, A. bonilla, F. Martinez-Gimenez, and A. Peris.

Abstract: We study Li-Yorke chaos and distributional chaos for operators on Banach spaces. More precisely, we characterize Li-Yorke chaos in terms of the existence of irregular vectors. Sufficient ``computable'' criteria for distributional and Li-Yorke chaos are given, together with the existence of dense scrambled sets under some additional conditions. We also obtain certain spectral properties. Finally, we show that every infinite dimensional separable Banach space admits a distributionally chaotic operator which is also hypercyclic.

Archive classification: math.FA

Mathematics Subject Classification: 47A16

Submitted from: tbermude@ull.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1005.3634

or

http://arXiv.org/abs/1005.3634