For each real number λ∈ [0, 1], λ-power distributional chaos has been in- troduced and studied via Furstenberg families recently. The chaoticity gets stronger and stronger as A varies from 1 to 0, where 1-power dis...For each real number λ∈ [0, 1], λ-power distributional chaos has been in- troduced and studied via Furstenberg families recently. The chaoticity gets stronger and stronger as A varies from 1 to 0, where 1-power distributional chaos is exactly the usual distributional chaos. As a generalization of distributional n-chaos,λ-power distributional n-chaos is defined similarly. Lots of classic results on distributional chaos can be improved to be the versions of λ-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 λ∈ [0, 1], ）,-power distributional n-chaos can still appear in minimal systems with zero topological entropy.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11071084,11201157,11471125)the Natural Science Foundation of Guangdong Province(No.S2013040013857)
文摘For each real number λ∈ [0, 1], λ-power distributional chaos has been in- troduced and studied via Furstenberg families recently. The chaoticity gets stronger and stronger as A varies from 1 to 0, where 1-power distributional chaos is exactly the usual distributional chaos. As a generalization of distributional n-chaos,λ-power distributional n-chaos is defined similarly. Lots of classic results on distributional chaos can be improved to be the versions of λ-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 λ∈ [0, 1], ）,-power distributional n-chaos can still appear in minimal systems with zero topological entropy.
