Distributional chaos for backward shifts
By Félix Martínez-Giménez, Piotr Oprocha, Alfredo Peris. 2009
74 citations recorded by the source corpus.
We provide sufficient conditions which give uniform distributional chaos for backward shift operators. We also compare distributional chaos with other well-studied notions of chaos for linear operators, like Devaney chaos and hypercyclicity, and show that Devaney chaos implies uniform distributional chaos for weighted backward shifts, but there are examples of backward shifts which are uniformly distributionally chaotic and not hypercyclic.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c78899a5b7b96bade04bf8d919e556ccea82d898
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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 Mathematical Physics
- Alfredo Peris
- Antonio Bonilla
- Nilson C. Bernardes
- Félix Martínez-Giménez
- Vladimír Müller
- Piotr Oprocha
- Tatjana Eisner
- Quentin Menet
Citations in the corpus
- Distributional chaos for operators with full scrambled sets (2013, background): “We should point out that it is easy to construct non-hypercyclic but distributionally chaotic unilateral shifts (see [14]).”
- Distributional chaos for linear operators (2013, background): “They were considered for linear operators on Banach or Fréchet spaces in [6, 12, 13, 14, 16, 17, 20, 24].”