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Moreover, we show that if the evolution equation has an inertial manifold, then the dynamics of the evolution equation is equivalent to the dynamics of the projection of the solutions on the finite-dimensional space spanned by the approximating polynomials. Our results suggest that certain numerical schemes may capture the essential dynamics of the underlying evolution equation.<\/p>","DOI":"10.1090\/s0025-5718-97-00850-8","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"1073-1087","source":"Crossref","is-referenced-by-count":78,"title":["Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems"],"prefix":"10.1090","volume":"66","author":[{"given":"Bernardo","family":"Cockburn","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Don","family":"Jones","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Edriss","family":"Titi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[1997]]},"reference":[{"issue":"4","key":"1","first-page":"133","article-title":"Attractors of evolution partial differential equations and estimates of their dimension","volume":"38","author":"Babin, A. 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