{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T15:30:11Z","timestamp":1759073411837,"version":"3.37.3"},"reference-count":20,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11001038","DC120101112"],"award-info":[{"award-number":["11001038","DC120101112"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["11001038","DC120101112"],"award-info":[{"award-number":["11001038","DC120101112"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>Consider the surjective, continuous map<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>f<\/mml:mi><mml:mo>:<\/mml:mo><mml:mi>X<\/mml:mi><mml:mo>\u2192<\/mml:mo><mml:mi>X<\/mml:mi><\/mml:math>and the continuous map<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mover accent=\"false\"><mml:mrow><mml:mi>f<\/mml:mi><\/mml:mrow><mml:mo>\u00af<\/mml:mo><\/mml:mover><\/mml:mrow><\/mml:math>of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mi>\ud835\udca6<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>X<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>induced by<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>f<\/mml:mi><\/mml:mrow><\/mml:math>, where<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi>X<\/mml:mi><\/mml:mrow><\/mml:math>is a compact metric space and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mi>\ud835\udca6<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>X<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>is the space of all nonempty compact subsets of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mrow><mml:mi>X<\/mml:mi><\/mml:mrow><\/mml:math>endowed with the Hausdorff metric. In this paper, we give a short proof that if<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mrow><mml:mover accent=\"false\"><mml:mrow><mml:mi>f<\/mml:mi><\/mml:mrow><mml:mo>\u00af<\/mml:mo><\/mml:mover><\/mml:mrow><\/mml:math>is Li-Yoke sensitive, then<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:mrow><mml:mi>f<\/mml:mi><\/mml:mrow><\/mml:math>is Li-Yorke sensitive. Furthermore, we give an example showing that Li-Yorke sensitivity of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><mml:mrow><mml:mi>f<\/mml:mi><\/mml:mrow><\/mml:math>does not imply Li-Yorke sensitivity of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\"><mml:mrow><mml:mover accent=\"false\"><mml:mrow><mml:mi>f<\/mml:mi><\/mml:mrow><mml:mo>\u00af<\/mml:mo><\/mml:mover><\/mml:mrow><\/mml:math>.<\/jats:p>","DOI":"10.1155\/2013\/260856","type":"journal-article","created":{"date-parts":[[2013,12,9]],"date-time":"2013-12-09T21:01:23Z","timestamp":1386622883000},"page":"1-5","source":"Crossref","is-referenced-by-count":7,"title":["Li-Yorke Sensitivity of Set-Valued Discrete Systems"],"prefix":"10.1155","volume":"2013","author":[{"given":"Heng","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Dalian University of Technology, Dalian, Liaoning 116600, China"},{"name":"Department of Mathematics, Dalian Nationalities University, Dalian, Liaoning 116600, China"}]},{"given":"Fengchun","family":"Lei","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Dalian University of Technology, Dalian, Liaoning 116600, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0408-2157","authenticated-orcid":true,"given":"Lidong","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Dalian Nationalities University, Dalian, Liaoning 116600, China"}]}],"member":"311","reference":[{"key":"5a","doi-asserted-by":"publisher","DOI":"10.1007\/BF01646553"},{"key":"5b","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/BF01893621","volume":"23","year":"1971","journal-title":"Communications in Mathematical Physics"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.2748\/tmj\/1178229634"},{"year":"1989","key":"17"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.2307\/2318254"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/16\/4\/313"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1515\/crll.2002.053"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(02)00406-X"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.06.039"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.12.039"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.12.033"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/s11425-004-5234-5"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.11.006"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.11.089"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.10.041"},{"key":"19","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/BF01585664","volume":"79","year":"1975","journal-title":"Monatshefte f\u00fcr Mathematik"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2009.06.003"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2010.05.002"},{"year":"1995","series-title":"Studies in Advanced Mathematics","key":"3"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.2307\/1999705"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/260856.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/260856.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/260856.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,11]],"date-time":"2020-05-11T17:31:02Z","timestamp":1589218262000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/260856\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":20,"alternative-id":["260856","260856"],"URL":"https:\/\/doi.org\/10.1155\/2013\/260856","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}