{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:31:32Z","timestamp":1787232692188,"version":"build-2736575974"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>We study the extent to which properties of infinite-dimensional dynamical systems can be accurately detected by examining observations of such systems. Let H be a separable Hilbert space. Let $f:H\\to H$ be a map, and let $A\\subset H$ be a compact set satisfying $f(A)=A$. We prove that, for almost every (in the sense of prevalence) continuous observable $\\varphi:H\\to\\mathbb{R}^{M}$, if f induces a map $\\bar{f}$ satisfying $\\bar{f}\\circ\\varphi=\\varphi\\circ f$ on A and if this induced map has certain properties, then the observable $\\varphi$ is one-to-one on A, and therefore the dynamics of f on A are topologically conjugate to those of $\\bar{f}$ on $\\varphi(A)$.<\/jats:p>","DOI":"10.1137\/090760210","type":"journal-article","created":{"date-parts":[[2010,11,5]],"date-time":"2010-11-05T20:13:40Z","timestamp":1288988020000},"page":"1229-1243","source":"Crossref","is-referenced-by-count":3,"title":["Observing Infinite-dimensional Dynamical Systems"],"prefix":"10.1137","volume":"9","author":[{"given":"Jessica","family":"Lin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"William","family":"Ott","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,11,4]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"articl","DOI":"10.2202\/1534-5963.1003","volume":"1","author":"Anderson R. M.","year":"2001","journal-title":"B. E. J. Theoret. Econ."},{"key":"R2","unstructured":"A. V. Babin and M. I. Vishik,\n                      Attractors of Evolution Equations\n                      translated and revised from the 1989 Russian original by Babin, Studies Math. Appl. 25, North\u2013Holland, Amsterdam, 1992."},{"key":"R3","unstructured":"V. V. Chepyzhov and M. I. Vishik,\n                      Attractors for Equations of Mathematical Physics\n                      , Amer. Math. Soc. Colloq. Publ. 49, American Mathematical Society, Providence, RI, 2002."},{"key":"R4","first-page":"255","volume":"13","author":"Christensen J. P. R.","year":"1973","journal-title":"in Proceedings of the International Symposium on Partial Differential Equations and the Geometry of Normed Linear Spaces (Jerusalem, 1972), Israel J. Math."},{"key":"R5","doi-asserted-by":"crossref","unstructured":"C. R. Doering and J. D. Gibbon,\n                      Applied Analysis of the Navier\u2013Stokes Equations\n                      , Cambridge Texts Appl. Math., Cambridge University Press, Cambridge, UK, 1995.","DOI":"10.1017\/CBO9780511608803"},{"key":"R6","unstructured":"A. Eden, C. Foias, B. Nicolaenko, and R. Temam,\n                      Exponential Attractors for Dissipative Evolution Equations\n                      , Res. Appl. Math. 37, Masson, Paris, 1994."},{"key":"R7","unstructured":"J. K. Hale,\n                      Asymptotic Behavior of Dissipative Systems\n                      , Math. 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Robinson,\n                      Infinite-Dimensional Dynamical Systems. An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors\n                      , Cambridge Texts Appl. Math., Cambridge University Press, Cambridge, UK, 2001."},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/22\/4\/001"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2005.04.009"},{"key":"R20","doi-asserted-by":"crossref","unstructured":"G. R. Sell and Y. You,\n                      Dynamics of Evolutionary Equations\n                      , Appl. Math. Sci. 143, Springer-Verlag, New York, 2002.","DOI":"10.1007\/978-1-4757-5037-9"},{"key":"R21","doi-asserted-by":"crossref","unstructured":"R. Temam,\n                      Infinite-Dimensional Dynamical Systems in Mechanics and Physics\n                      , 2nd ed., Appl. Math. Sci. 68, Springer-Verlag, New York, 1997.","DOI":"10.1007\/978-1-4612-0645-3"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1969-0245916-7"}],"container-title":["SIAM Journal on Applied Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/090760210","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:16:09Z","timestamp":1787231769000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/090760210"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/090760210"],"URL":"https:\/\/doi.org\/10.1137\/090760210","relation":{},"ISSN":["1536-0040"],"issn-type":[{"value":"1536-0040","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}