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We compare four different notions of chaos in zero-dimensional systems (subshifts). We provide examples showing that in that case positive topological entropy does not imply strong chaos, strong chaos does not imply complicated dynamics at all, and ω-chaos does not imply Li-Yorke chaos.
Rafał Pikuła. "On some notions of chaos in dimension zero." Colloquium Mathematicae 107.2 (2007): 167-177. <http://eudml.org/doc/284047>.
@article{RafałPikuła2007, abstract = {We compare four different notions of chaos in zero-dimensional systems (subshifts). We provide examples showing that in that case positive topological entropy does not imply strong chaos, strong chaos does not imply complicated dynamics at all, and ω-chaos does not imply Li-Yorke chaos.}, author = {Rafał Pikuła}, journal = {Colloquium Mathematicae}, keywords = {Li–Yorke chaos; strong chaos; -chaos; topological entropy}, language = {eng}, number = {2}, pages = {167-177}, title = {On some notions of chaos in dimension zero}, url = {http://eudml.org/doc/284047}, volume = {107}, year = {2007}, }
TY - JOUR AU - Rafał Pikuła TI - On some notions of chaos in dimension zero JO - Colloquium Mathematicae PY - 2007 VL - 107 IS - 2 SP - 167 EP - 177 AB - We compare four different notions of chaos in zero-dimensional systems (subshifts). We provide examples showing that in that case positive topological entropy does not imply strong chaos, strong chaos does not imply complicated dynamics at all, and ω-chaos does not imply Li-Yorke chaos. LA - eng KW - Li–Yorke chaos; strong chaos; -chaos; topological entropy UR - http://eudml.org/doc/284047 ER -