{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T13:29:55Z","timestamp":1789046995760,"version":"build-2803163510"},"reference-count":14,"publisher":"AIP Publishing","issue":"9","funder":[{"DOI":"10.13039\/501100004488","name":"Hrvatska Zaklada za Znanost","doi-asserted-by":"publisher","award":["MOBODL-2023-08-4960"],"award-info":[{"award-number":["MOBODL-2023-08-4960"]}],"id":[{"id":"10.13039\/501100004488","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004488","name":"Hrvatska Zaklada za Znanost","doi-asserted-by":"publisher","award":["IP-2022-10-9820 GLODS"],"award-info":[{"award-number":["IP-2022-10-9820 GLODS"]}],"id":[{"id":"10.13039\/501100004488","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004488","name":"Hrvatska Zaklada za Znanost","doi-asserted-by":"publisher","award":["UIP-2025-02-4309 ToGeCoP"],"award-info":[{"award-number":["UIP-2025-02-4309 ToGeCoP"]}],"id":[{"id":"10.13039\/501100004488","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100020668","name":"European Research Executive Agency","doi-asserted-by":"publisher","award":["101183111- DSYREKI-HORIZON-MSCA-2023-SE-01"],"award-info":[{"award-number":["101183111- DSYREKI-HORIZON-MSCA-2023-SE-01"]}],"id":[{"id":"10.13039\/100020668","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,9,1]]},"abstract":"<jats:p>For the Lozi map La,b, we consider parameter pairs for which the fixed point X has no homoclinic points and the period-two orbit {P, P\u2032} is attracting. For such parameters, let \u2113 be the set of accumulation points of the unstable manifold WXu that do not lie on WXu. We construct a polygon D whose forward images under La,b form nested sequences of sets that eventually become trapping. We show that this geometric construction gives a characterization of \u2113 as the intersection of these iterates. Using this structure, we prove that the non-wandering set for La,b2 is contained in the union of \u2113 and the set of fixed points of La,b. As a consequence, the Lozi map, restricted to the complement of \u2113 in the plane, has zero topological entropy. This result extends a recent one of Misiurewicz and \u0160timac to a broader set of parameters.<\/jats:p>","DOI":"10.1063\/5.0344038","type":"journal-article","created":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T12:57:37Z","timestamp":1789045057000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Accumulation sets and zero entropy dynamics in the Lozi map"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-6305-0818","authenticated-orcid":false,"given":"Kristijan","family":"Kilassa Kvaternik","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Faculty of Electrical Engineering and Computing, University of Zagreb , Unska 3, 10\u2009000 Zagreb, and , ul. prof. Stanis\u0142awa \u0141ojasiewicza 6, 30-348 Krak\u00f3w,","place":["Croatia Poland"]},{"name":"Institute of Mathematics, Jagiellonian University , Unska 3, 10\u2009000 Zagreb, and , ul. prof. Stanis\u0142awa \u0141ojasiewicza 6, 30-348 Krak\u00f3w,","place":["Croatia Poland"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,9,10]]},"reference":[{"issue":"Coll. C5","key":"2026091008573208400_c1","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1051\/jphyscol:1978505","article-title":"Un attracteur \u00e9trange du type attracteur de H\u00e9non","volume":"39","year":"1978","journal-title":"J. Phys."},{"key":"2026091008573208400_c2","doi-asserted-by":"publisher","first-page":"1783","DOI":"10.1017\/S0143385711000411","article-title":"Discontinuity of topological entropy for the Lozi maps","volume":"32","year":"2012","journal-title":"Ergod. Theory Dyn. 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Sci."},{"key":"2026091008573208400_c9","unstructured":"K.\n            Kilassa Kvaternik\n          , \u201cTangential homoclinic points locus of the Lozi maps and applications,\u201d Doctoral thesis (University of Zagreb, Croatia, 2022), Available online: https:\/\/repozitorij.pmf.unizg.hr\/islandora\/object\/pmf:11546"},{"key":"2026091008573208400_c10","volume-title":"Introduction to Dynamical Systems","year":"2002"},{"key":"2026091008573208400_c11","volume-title":"Introduction to the Modern Theory of Dynamical Systems","year":"1995"},{"key":"2026091008573208400_c12","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1017\/S0143385700006702","article-title":"A new proof of the Brouwer plane translation theorem","volume":"12","year":"1992","journal-title":"Ergod. Theory Dyn. Syst."},{"key":"2026091008573208400_c13","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-026-10505-2","article-title":"Tangential homoclinic points for Lozi maps","year":"2026","journal-title":"J. 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