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 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
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 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>).
