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| On λ-Power Distributional n-Chaos |
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Citation： |
Heman FU,Feng TAN.On λ-Power Distributional n-Chaos[J].Chinese Annals of Mathematics B,2017,38(5):1119~1130 |
| Page view： 2778
Net amount： 1130 |
Authors： |
Heman FU; Feng TAN |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11071084, 11201157, 11471125) and the
Natural Science Foundation of Guangdong Province
(No.S2013040013857). |
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| Abstract： |
For each real number $\lambda\in[0,1]$, $\lambda$-power
distributional chaos has been introduced and studied via Furstenberg
families recently. The chaoticity gets stronger and stronger as
$\lambda$ varies from 1 to 0, where 1-power distributional chaos is
exactly the usual distributional chaos. As a generalization of
distributional $n$-chaos, $\lambda$-power distributional $n$-chaos
is defined similarly. Lots of classic results on distributional
chaos can be improved to be the versions of $\lambda$-power
distributional $n$-chaos accordingly. A practical method for
distinguishing $0$-power distributional $n$-chaos is given. A
transitive system is constructed to be 0-power distributionally
$n$-chaotic but without any distributionally $(n+1)$-scrambled
tuples. For each $\lambda\in[0,1]$, $\lambda$-power
distributional $n$-chaos can still appear in minimal systems with
zero topological entropy. |
Keywords： |
Furstenberg family, $\lambda$-power distributional $n$-chaos, Minimal system, Topological entropy |
Classification： |
54H20, 37B05, 37B10, 37B40 |
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