{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,6,28]],"date-time":"2022-06-28T23:46:53Z","timestamp":1656460013544},"reference-count":21,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2014,2]]},"abstract":"<jats:p>We consider six properties of continuous maps, such as the existence of an arc horseshoe, the positivity of topological entropy, the existence of a homoclinic trajectory, or Lyapunov instability on the set of periodic points. The relations between the considered properties are provided in the case of graph maps, dendrite maps and maps on compact metric spaces. For example, by [Llibre &amp; Misiurewicz, 1993] in the case of graph maps, the existence of an arc horseshoe implies the positivity of topological entropy, but we construct a continuous map on a Peano continuum with an arc horseshoe and zero topological entropy. We also formulate one open problem.<\/jats:p>","DOI":"10.1142\/s0218127414500163","type":"journal-article","created":{"date-parts":[[2014,3,7]],"date-time":"2014-03-07T03:58:02Z","timestamp":1394164682000},"page":"1450016","source":"Crossref","is-referenced-by-count":2,"title":["Horseshoes, Entropy, Homoclinic Trajectories, and Lyapunov Stability"],"prefix":"10.1142","volume":"24","author":[{"given":"Zden\u011bk","family":"Ko\u010dan","sequence":"first","affiliation":[{"name":"Mathematical Institute in Opava, Silesian University in Opava, Na Rybn\u00ed\u010dku 1, 746 01 Opava, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Veronika","family":"Kurkov\u00e1","sequence":"additional","affiliation":[{"name":"Mathematical Institute in Opava, Silesian University in Opava, Na Rybn\u00ed\u010dku 1, 746 01 Opava, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michal","family":"M\u00e1lek","sequence":"additional","affiliation":[{"name":"Mathematical Institute in Opava, Silesian University in Opava, Na Rybn\u00ed\u010dku 1, 746 01 Opava, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2014,3,6]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/1980"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1993-1043403-3"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1978-0509258-X"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0086977"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0084762"},{"key":"rf6","doi-asserted-by":"crossref","first-page":"969","DOI":"10.3934\/dcds.2003.9.969","volume":"9","author":"Blokh A.","journal-title":"Discr. Contin. Dyn. Syst."},{"key":"rf7","unstructured":"A.\u00a0Blokh, C.\u00a0Cleveland and M.\u00a0Misiurewicz, Modern Dynamical Systems and Applications (Cambridge University Press, Cambridge, 2004)\u00a0pp. 253\u2013270."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1971-0274707-X"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127411028295"},{"key":"rf10","first-page":"19","volume":"190","author":"Dinaburg E. I.","journal-title":"Dokl. Akad. Nauk. SSSR"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.2307\/1967832"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1967-0207959-1"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2013.07.026"},{"key":"rf14","first-page":"181","volume":"13","author":"Ko\u010dan Z.","journal-title":"Ann. Math. Sil."},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385709001011"},{"key":"rf16","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1017\/S0143385700007082","volume":"12","author":"Kolyada S. F.","journal-title":"Ergod. Th. Dyn. Syst."},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1016\/0040-9383(93)90014-M"},{"key":"rf18","first-page":"167","volume":"27","author":"Misiurewicz M.","journal-title":"Bull. Acad. Pol. Sci., S\u00e9r. Sci. Math."},{"key":"rf19","series-title":"Monographs and Textbooks in Pure and Applied Mathematics","doi-asserted-by":"crossref","DOI":"10.1201\/9781315274089","volume-title":"Continuum Theory. An Introduction","volume":"158","author":"Nadler S. B.","year":"1992"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-8897-3"},{"key":"rf21","first-page":"265","volume":"70","author":"\u0160indel\u00e1\u0159ov\u00e1 P.","journal-title":"Acta Math. Univ. Comenianae"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127414500163","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,16]],"date-time":"2020-08-16T02:43:52Z","timestamp":1597545832000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127414500163"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,2]]},"references-count":21,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2014,3,6]]},"published-print":{"date-parts":[[2014,2]]}},"alternative-id":["10.1142\/S0218127414500163"],"URL":"https:\/\/doi.org\/10.1142\/s0218127414500163","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,2]]}}}