{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T11:25:55Z","timestamp":1778671555979,"version":"3.51.4"},"reference-count":5,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T00:00:00Z","timestamp":1556668800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>For an    \u03b1   -expansive homeomorphism of a compact space we give an elementary proof of the following well-known result in topological dynamics: A sufficient condition for the homeomorphism to have the shadowing property is that it has the    \u03b1   -shadowing property for one-jump pseudo orbits (known as the local product structure property). The proof relies on a reformulation of the property of expansiveness in terms of the pseudo orbits of the system.<\/jats:p>","DOI":"10.3390\/axioms8020054","type":"journal-article","created":{"date-parts":[[2019,5,2]],"date-time":"2019-05-02T03:15:22Z","timestamp":1556766922000},"page":"54","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Note on Anosov Homeomorphisms"],"prefix":"10.3390","volume":"8","author":[{"given":"Mauricio","family":"Achigar","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica y Estad\u00edstica del Litoral, Universidad de la Rep\u00fablica, Gral. Rivera 1350, Salto 50000, Uruguay"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,1]]},"reference":[{"key":"ref_1","unstructured":"Aoki, N., and Hiraide, K. (1994). Topological Theory of Dynamical Systems, Elsevier."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/BF02125125","article-title":"Expansiveness, hyperbolicity and Hausdorff dimension","volume":"126","author":"Fathi","year":"2005","journal-title":"Commun. Math. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1090\/S0002-9939-1950-0038022-3","article-title":"Unstable homeomorphisms","volume":"1","author":"Utz","year":"1950","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1080\/00029890.1962.11989902","article-title":"Expansive self-homeomorphisms of a compact metric space","volume":"69","author":"Bryant","year":"1962","journal-title":"Am. Math. Mon."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/BFb0101795","article-title":"On the pseudo orbit tracing property and its relationship to stability","volume":"668","author":"Walters","year":"1978","journal-title":"Struct. Attractors Dyn. Syst."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/8\/2\/54\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:48:37Z","timestamp":1760186917000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/8\/2\/54"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,1]]},"references-count":5,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,6]]}},"alternative-id":["axioms8020054"],"URL":"https:\/\/doi.org\/10.3390\/axioms8020054","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,1]]}}}