{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T01:20:14Z","timestamp":1783041614660,"version":"3.54.6"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,3,7]],"date-time":"2019-03-07T00:00:00Z","timestamp":1551916800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2019,6]]},"DOI":"10.1007\/s00211-019-01031-z","type":"journal-article","created":{"date-parts":[[2019,3,7]],"date-time":"2019-03-07T08:07:22Z","timestamp":1551946042000},"page":"421-463","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Spectral Galerkin methods for transfer operators in uniformly expanding dynamics"],"prefix":"10.1007","volume":"142","author":[{"given":"Caroline","family":"Wormell","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,3,7]]},"reference":[{"key":"1031_CR1","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1145\/2998442","volume":"43","author":"JL Aurentz","year":"2017","unstructured":"Aurentz, J.L., Trefethen, L.N.: Chopping a Chebyshev series. ACM Trans. Math. Softw. (TOMS) 43, 33 (2017)","journal-title":"ACM Trans. Math. Softw. (TOMS)"},{"key":"1031_CR2","doi-asserted-by":"publisher","first-page":"1486","DOI":"10.1007\/s10955-016-1523-y","volume":"163","author":"W Bahsoun","year":"2016","unstructured":"Bahsoun, W., Galatolo, S., Nisoli, I., Niu, X.: Rigorous approximation of diffusion coefficients for expanding maps. J. Stat. Phys. 163, 1486\u20131503 (2016)","journal-title":"J. Stat. Phys."},{"key":"1031_CR3","doi-asserted-by":"publisher","first-page":"1073","DOI":"10.1088\/1361-6544\/aa9a88","volume":"31","author":"W Bahsoun","year":"2018","unstructured":"Bahsoun, W., Galatolo, S., Nisoli, I., Niu, X.: A rigorous computational approach to linear response. Nonlinearity 31, 1073 (2018)","journal-title":"Nonlinearity"},{"key":"1031_CR4","doi-asserted-by":"publisher","first-page":"525","DOI":"10.1088\/0951-7715\/12\/3\/006","volume":"12","author":"V Baladi","year":"1999","unstructured":"Baladi, V., Holschneider, M.: Approximation of nonessential spectrum of transfer operators. Nonlinearity 12, 525 (1999)","journal-title":"Nonlinearity"},{"key":"1031_CR5","volume-title":"Chebyshev and Fourier Spectral Methods","author":"JP Boyd","year":"2001","unstructured":"Boyd, J.P.: Chebyshev and Fourier Spectral Methods. Courier Corporation, Mineola (2001)"},{"key":"1031_CR6","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1007\/978-3-642-56589-2_7","volume-title":"Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems","author":"M Dellnitz","year":"2001","unstructured":"Dellnitz, M., Froyland, G., Junge, O.: The algorithms behind GAIO\u2013set oriented numerical methods for dynamical systems. In: Fiedler, B. (ed.) Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, pp. 145\u2013174. Springer, Berlin (2001)"},{"key":"1031_CR7","first-page":"671","volume":"17","author":"G Froyland","year":"2007","unstructured":"Froyland, G.: On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps. Dyn. Syst. 17, 671\u2013689 (2007)","journal-title":"Dyn. Syst."},{"key":"1031_CR8","doi-asserted-by":"publisher","first-page":"2435","DOI":"10.1088\/0951-7715\/24\/9\/003","volume":"24","author":"G Froyland","year":"2011","unstructured":"Froyland, G., Murray, R., Stancevic, O.: Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity 24, 2435 (2011)","journal-title":"Nonlinearity"},{"key":"1031_CR9","doi-asserted-by":"publisher","first-page":"958","DOI":"10.1137\/130911044","volume":"13","author":"S Galatolo","year":"2014","unstructured":"Galatolo, S., Nisoli, I.: An elementary approach to rigorous approximation of invariant measures. SIAM J. Appl. Dyn. Syst. 13, 958\u2013985 (2014)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"1031_CR10","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/j.physd.2016.05.010","volume":"331","author":"GA Gottwald","year":"2016","unstructured":"Gottwald, G.A., Wormell, J.P., Wouters, J.: On spurious detection of linear response and misuse of the fluctuation\u2013dissipation theorem in finite time series. Physica D Nonlinear Phenom. 331, 89\u2013101 (2016)","journal-title":"Physica D Nonlinear Phenom."},{"key":"1031_CR11","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1007\/s00440-003-0300-4","volume":"128","author":"S Gou\u00ebzel","year":"2004","unstructured":"Gou\u00ebzel, S.: Central limit theorem and stable laws for intermittent maps. Probab. Theory Relat. Fields 128, 82\u2013122 (2004)","journal-title":"Probab. Theory Relat. Fields"},{"key":"1031_CR12","doi-asserted-by":"crossref","unstructured":"Hansen, A.C.: Infinite-dimensional numerical linear algebra: theory and applications, In: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, The Royal Society, p.\u00a0rspa20090617 (2010)","DOI":"10.1098\/rspa.2009.0617"},{"key":"1031_CR13","unstructured":"Holschneider, M.: Wavelet analysis of transfer operators acting on n-dimensional H\u00f6lder, Zygmund Triebel spaces. Preprint \n                    https:\/\/web.ma.utexas.edu\/mp_arc-bin\/mpa?yn=96-169\n                    \n                   (1996)"},{"key":"1031_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.aim.2003.09.011","volume":"192","author":"O Jenkinson","year":"2005","unstructured":"Jenkinson, O., Pollicott, M.: Orthonormal expansions of invariant densities for expanding maps. Adv. Math. 192, 1\u201334 (2005)","journal-title":"Adv. Math."},{"key":"1031_CR15","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/s10955-017-1930-8","volume":"170","author":"O Jenkinson","year":"2018","unstructured":"Jenkinson, O., Pollicott, M., Vytnova, P.: Rigorous computation of diffusion coefficients for expanding maps. J. Stat. Phys. 170, 221\u2013253 (2018)","journal-title":"J. Stat. Phys."},{"key":"1031_CR16","unstructured":"Korepanov, A., Kosloff, Z., Melbourne, I.: Explicit coupling argument for uniformly expanding maps, arXiv preprint \n                    arXiv:1602.03795\n                    \n                   (2016)"},{"key":"1031_CR17","doi-asserted-by":"publisher","first-page":"1007","DOI":"10.3934\/dcds.2010.26.1007","volume":"26","author":"R Murray","year":"2010","unstructured":"Murray, R.: Ulam\u2019s method for some non-uniformly expanding maps. Discrete Contin. Dyn. Syst. 26, 1007\u20131018 (2010)","journal-title":"Discrete Contin. Dyn. Syst."},{"key":"1031_CR18","unstructured":"Olver, S.: ApproxFun. Available at \n                    http:\/\/github.com\/JuliaApproximation\/ApproxFun.jl\n                    \n                   and in the Julia package repository"},{"key":"1031_CR19","doi-asserted-by":"publisher","first-page":"462","DOI":"10.1137\/120865458","volume":"55","author":"S Olver","year":"2013","unstructured":"Olver, S., Townsend, A.: A fast and well-conditioned spectral method. SIAM Rev. 55, 462\u2013489 (2013)","journal-title":"SIAM Rev."},{"key":"1031_CR20","unstructured":"Revels, J., Lubin, M., Papamarkou, T.: Forward-mode automatic differentiation in Julia, \n                    arXiv:1607.07892\n                    \n                   [cs.MS] (2016)"},{"key":"1031_CR21","volume-title":"Approximation Theory and Approximation Practice","author":"LN Trefethen","year":"2013","unstructured":"Trefethen, L.N.: Approximation Theory and Approximation Practice. Siam, Philadelphia (2013)"},{"key":"1031_CR22","unstructured":"Wormell, C.: Poltergeist. Available at \n                    http:\/\/github.com\/wormell\/Poltergeist.jl\n                    \n                   and in the Julia package repository"}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-019-01031-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-019-01031-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-019-01031-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,3,6]],"date-time":"2020-03-06T00:09:48Z","timestamp":1583453388000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-019-01031-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,7]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,6]]}},"alternative-id":["1031"],"URL":"https:\/\/doi.org\/10.1007\/s00211-019-01031-z","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,7]]},"assertion":[{"value":"6 March 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 January 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 March 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}