Li–Yorke and distributionally chaotic operators
By Teresa Bermúdez, Antonio Bonilla, Félix Martínez-Giménez, Alfredo Peris. 2010
130 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/4ebc72b7dabb7c62abec3b0418dbbf34145fcbe9
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In Applied Mathematics
- Alfredo Peris
- Nilson C. Bernardes
- Antonio Bonilla
- Vladimír Müller
- Félix Martínez-Giménez
- Piotr Oprocha
- S. Grivaux
- Quentin Menet
In Geometry and Topology
- Alfredo Peris
- Antonio Bonilla
- Piotr Oprocha
- Nilson C. Bernardes
- S. Grivaux
- N. Feldman
- Stanislav Shkarin
Citations in the corpus
- Li–Yorke chaos in linear dynamics (2014, background): “Let us observe that the above criterion is slightly different from the Li–Yorke chaos criterion defined in [5] in the context of Banach spaces.”
- Chaotic Behaviour of the Solutions of the Moore-Gibson- Thompson Equation (2015, unknown): “8], see also [4].”
- Distributional chaos for operators with full scrambled sets (2013, background): “introduced in [4] the following notion:”