{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T16:10:56Z","timestamp":1760199056323,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T00:00:00Z","timestamp":1544140800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"JSPS KAKENHI","award":["16K05167"],"award-info":[{"award-number":["16K05167"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, the notion of shadowable measures is introduced as a generalization of the shadowing property from the measure theoretical view point, and the set of diffeomorphisms satisfying the notion is considered. The dynamics of the     C 1    -interior of the set of diffeomorphisms possessing the shadowable measures is characterized as the uniform hyperbolicity.<\/jats:p>","DOI":"10.3390\/axioms7040093","type":"journal-article","created":{"date-parts":[[2018,12,10]],"date-time":"2018-12-10T03:36:41Z","timestamp":1544413001000},"page":"93","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Diffeomorphisms with Shadowable Measures"],"prefix":"10.3390","volume":"7","author":[{"given":"Kazumine","family":"Moriyasu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Tokushima University, Tokushima 770-8502, Japan"}]},{"given":"Kazuhiro","family":"Sakai","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Utsunomiya University, Utsunomiya 321-8505, Japan"}]},{"given":"Naoya","family":"Sumi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kumamoto University, Kumamoto 860-8555, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,7]]},"reference":[{"key":"ref_1","unstructured":"Morales, C.A., and Sirvent, V.F. (2013). Expansive measures. IMPA Mathematical Publications 29, Col\u00f3quio Brasileiro de Matem\u00e1tica, Instituto Nacional de Matem\u00e1tica Pura e Aplicada."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3467","DOI":"10.1016\/j.jde.2016.04.029","article-title":"Topological stability and pseudo-orbit tracing property for expansive measures","volume":"262","author":"Lee","year":"2017","journal-title":"J. Differ. Eq."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1090\/S0002-9939-2014-12296-9","article-title":"On measure expansive diffeomorphisms","volume":"143","author":"Pacifico","year":"2015","journal-title":"Proc. Amer. Math. Soc."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1016\/j.jmaa.2014.01.023","article-title":"Measure-expansive diffeomorphisms","volume":"414","author":"Sakai","year":"1994","journal-title":"J. Math. Anal. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Pilyugin, S.Y., and Sakai, K. (2017). Shadowing and Hyperbolicity, Springer. Lecture Notes in Mathematics.","DOI":"10.1007\/978-3-319-65184-2"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1216\/RMJ-1977-7-3-425","article-title":"Stability theorems and hyperbolicity in dynamical systems","volume":"7","author":"Robinson","year":"1977","journal-title":"Rocky Mt. J. Math."},{"key":"ref_7","first-page":"373","article-title":"Pseudo orbit tracing property and strong transversality of diffeomorphisms on closed manifolds","volume":"31","author":"Sakai","year":"1994","journal-title":"Osaka J. Math."},{"key":"ref_8","unstructured":"Robinson, C. (1999). Dynamical Systems: Stability, Symbolic Dynamics, and Chaos, CRC Press. [2nd ed.]. Studies in Advanced Mathematics."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Denker, M., Grillenberger, C., and Sigmund, K. (1976). Ergodic Theory on Compact Spaces, Springer. Lecture Notes in Math.","DOI":"10.1007\/BFb0082364"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1017\/S0143385700006726","article-title":"Diffeomorphisms in \u21311(M) satisfy Axiom A","volume":"12","author":"Hayashi","year":"1992","journal-title":"Ergod. Th. Dynam. Sys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1134\/S0081543807010178","article-title":"C0 transversality and shadowing properties","volume":"256","author":"Pilyugin","year":"2007","journal-title":"Proc. Steklov Inst. Math."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1017\/S0027763000003664","article-title":"The topological stability of diffeomorphisms","volume":"123","author":"Moriyasu","year":"1991","journal-title":"Nagoya Math. J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1090\/S0002-9947-1971-0283812-3","article-title":"Necessary conditions for stability of diffeomorphisms","volume":"158","author":"Franks","year":"1971","journal-title":"Trans. Am. Math. Soc."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/7\/4\/93\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:31:58Z","timestamp":1760196718000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/7\/4\/93"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,7]]},"references-count":13,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,12]]}},"alternative-id":["axioms7040093"],"URL":"https:\/\/doi.org\/10.3390\/axioms7040093","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2018,12,7]]}}}