This paper focus on the chaotic properties of minimal subshift of shift operators. It is proved that the minimal subshift of shift operators is uniformly distributional chaotic, distributional chaotic in a sequence, d...This paper focus on the chaotic properties of minimal subshift of shift operators. It is proved that the minimal subshift of shift operators is uniformly distributional chaotic, distributional chaotic in a sequence, distributional chaotic of type k ( k∈{ 1,2,2 1 2 ,3 } ), and ( 0,1 ) -distribution.展开更多
This paper is concerned with the sensitivity of set-valued discrete systems. Firstly, this paper obtained the equivalence between <img src="Edit_7024f70b-0568-4ca8-a554-c0d05abc0df0.bmp" alt="" ...This paper is concerned with the sensitivity of set-valued discrete systems. Firstly, this paper obtained the equivalence between <img src="Edit_7024f70b-0568-4ca8-a554-c0d05abc0df0.bmp" alt="" />or <img src="Edit_95636a59-7d5d-4b6c-8bd5-f699dd9208df.bmp" alt="" /> and the product system <img src="Edit_c714caaf-0ed9-46bc-b3e1-b0223474a8f5.bmp" alt="" /> in sensitivity, infinite sensitivity, <em>F</em>-sensitivity, (<em>F</em><sub>1</sub>, <em>F</em><sub>2</sub>)-sensitivity. Then, the relation between (<em>X</em>, <em>f</em><sub>1,∞</sub>) or (<em>Y</em>, <em>g</em><sub>1,∞</sub>) and <img src="Edit_55b4ce47-89f3-4476-a8a8-4d4db5a4e8eb.bmp" alt="" /> in ergodic sensitivity is obtained. Where <img src="Edit_a99604c4-2f72-4e75-a998-8057b8790e03.bmp" alt="" /> is the set-valued dynamical system induced by a non-autonomous discrete dynamical system (<em>X</em>, <em>f</em><sub>1,∞</sub>).展开更多
Let <img alt="" src="Edit_6a94976d-35be-4dd4-b74f-d0bf6f497453.png" />be a non-autonomous discrete system and <img alt="" src="Edit_3516e048-3d23-4ae8-81ac-e7e732efbc89...Let <img alt="" src="Edit_6a94976d-35be-4dd4-b74f-d0bf6f497453.png" />be a non-autonomous discrete system and <img alt="" src="Edit_3516e048-3d23-4ae8-81ac-e7e732efbc89.png" /> be a set-valued discrete system induced by it. Where, <img alt="" src="Edit_f67612c1-bbf4-4c21-8b37-7d156ca9502d.png" />is the space formed by all non-empty compact subsets of <em>X</em> endowed with the Hausdorff metric <em>H</em>, <img alt="" src="Edit_cca16788-f64a-47c4-9645-e9c8cf9080fd.png" />is a set-valued mapping sequence induced by <img alt="" src="Edit_5a6d2e7f-3245-4dbd-98ec-dc977e23f3d8.png" />. It is proved that <img alt="" src="Edit_a25ef428-a2ff-46d5-9109-dcc67b57fbec.png" /> is <img alt="" src="Edit_ee8759ba-215c-4088-8590-db9f57eb4a7c.png" />-chaos, then <img alt="" src="Edit_f54b347a-033e-43e2-a3a1-d2fe5ac1f39d.png" />is <img alt="" src="Edit_72a57e59-dc43-4071-b0fe-432e379ddcc9.png" />-chaos. Where <img alt="" src="Edit_97813401-14af-4776-99fe-1e6cd08c3df1.png" />-chaos is denoted to <img alt="" src="Edit_9e2d88b4-7ece-430e-8978-800ff3280799.png" />-sensitive, <img alt="" src="Edit_440b79c1-f679-4571-b14d-6f804f402d75.png" />-sensitive, <img alt="" src="Edit_839b7b55-9961-4d80-b5cb-e7219a0ae871.png" />-transitive, <img alt="" src="Edit_feb0a032-255b-4cbd-b489-6a937c5a287a.png" />-accessible, <img alt="" src="Edit_3ba59c02-6df0-4ae1-8ac0-5c1b620e4a88.png" />-weakly mixing, <img alt="" src="Edit_7362ed03-8686-4cf7-94df-f0933b7abbff.png" />-<em>m</em>-sensitive, infinitely sensitive, or syndetically transitive.展开更多
This paper is concerned with some chaotic properties of a kind of coupled map lattices, which is proposed by Kaneko. First, this research discussed the sensitivity, infinite sensitivity, transitivity, accessibility, d...This paper is concerned with some chaotic properties of a kind of coupled map lattices, which is proposed by Kaneko. First, this research discussed the sensitivity, infinite sensitivity, transitivity, accessibility, densely Li-Yorke sensitivity and exact of coupled map lattices. Then, some sufficient conditions under which <img src="Edit_c0fc315a-d176-4c9e-9e41-5cb6bc6d679d.bmp" alt="" /> is Kato chaotic, positive entropy chaotic and Ruelle-Takens chaos are obtained.展开更多
文摘This paper focus on the chaotic properties of minimal subshift of shift operators. It is proved that the minimal subshift of shift operators is uniformly distributional chaotic, distributional chaotic in a sequence, distributional chaotic of type k ( k∈{ 1,2,2 1 2 ,3 } ), and ( 0,1 ) -distribution.
文摘This paper is concerned with the sensitivity of set-valued discrete systems. Firstly, this paper obtained the equivalence between <img src="Edit_7024f70b-0568-4ca8-a554-c0d05abc0df0.bmp" alt="" />or <img src="Edit_95636a59-7d5d-4b6c-8bd5-f699dd9208df.bmp" alt="" /> and the product system <img src="Edit_c714caaf-0ed9-46bc-b3e1-b0223474a8f5.bmp" alt="" /> in sensitivity, infinite sensitivity, <em>F</em>-sensitivity, (<em>F</em><sub>1</sub>, <em>F</em><sub>2</sub>)-sensitivity. Then, the relation between (<em>X</em>, <em>f</em><sub>1,∞</sub>) or (<em>Y</em>, <em>g</em><sub>1,∞</sub>) and <img src="Edit_55b4ce47-89f3-4476-a8a8-4d4db5a4e8eb.bmp" alt="" /> in ergodic sensitivity is obtained. Where <img src="Edit_a99604c4-2f72-4e75-a998-8057b8790e03.bmp" alt="" /> is the set-valued dynamical system induced by a non-autonomous discrete dynamical system (<em>X</em>, <em>f</em><sub>1,∞</sub>).
文摘Let <img alt="" src="Edit_6a94976d-35be-4dd4-b74f-d0bf6f497453.png" />be a non-autonomous discrete system and <img alt="" src="Edit_3516e048-3d23-4ae8-81ac-e7e732efbc89.png" /> be a set-valued discrete system induced by it. Where, <img alt="" src="Edit_f67612c1-bbf4-4c21-8b37-7d156ca9502d.png" />is the space formed by all non-empty compact subsets of <em>X</em> endowed with the Hausdorff metric <em>H</em>, <img alt="" src="Edit_cca16788-f64a-47c4-9645-e9c8cf9080fd.png" />is a set-valued mapping sequence induced by <img alt="" src="Edit_5a6d2e7f-3245-4dbd-98ec-dc977e23f3d8.png" />. It is proved that <img alt="" src="Edit_a25ef428-a2ff-46d5-9109-dcc67b57fbec.png" /> is <img alt="" src="Edit_ee8759ba-215c-4088-8590-db9f57eb4a7c.png" />-chaos, then <img alt="" src="Edit_f54b347a-033e-43e2-a3a1-d2fe5ac1f39d.png" />is <img alt="" src="Edit_72a57e59-dc43-4071-b0fe-432e379ddcc9.png" />-chaos. Where <img alt="" src="Edit_97813401-14af-4776-99fe-1e6cd08c3df1.png" />-chaos is denoted to <img alt="" src="Edit_9e2d88b4-7ece-430e-8978-800ff3280799.png" />-sensitive, <img alt="" src="Edit_440b79c1-f679-4571-b14d-6f804f402d75.png" />-sensitive, <img alt="" src="Edit_839b7b55-9961-4d80-b5cb-e7219a0ae871.png" />-transitive, <img alt="" src="Edit_feb0a032-255b-4cbd-b489-6a937c5a287a.png" />-accessible, <img alt="" src="Edit_3ba59c02-6df0-4ae1-8ac0-5c1b620e4a88.png" />-weakly mixing, <img alt="" src="Edit_7362ed03-8686-4cf7-94df-f0933b7abbff.png" />-<em>m</em>-sensitive, infinitely sensitive, or syndetically transitive.
文摘This paper is concerned with some chaotic properties of a kind of coupled map lattices, which is proposed by Kaneko. First, this research discussed the sensitivity, infinite sensitivity, transitivity, accessibility, densely Li-Yorke sensitivity and exact of coupled map lattices. Then, some sufficient conditions under which <img src="Edit_c0fc315a-d176-4c9e-9e41-5cb6bc6d679d.bmp" alt="" /> is Kato chaotic, positive entropy chaotic and Ruelle-Takens chaos are obtained.
