{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T11:44:03Z","timestamp":1776771843240,"version":"3.51.2"},"reference-count":35,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,28]],"date-time":"2014-03-28T00:00:00Z","timestamp":1395964800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2014,6]]},"abstract":"<jats:p>We discuss some recent results related to the deduction of a suitable probabilistic model for the description of the statistical features of a given deterministic dynamics. More precisely, we motivate and investigate the computability of invariant measures and some related concepts. We also present some experiments investigating the limits of naive simulations in dynamics.<\/jats:p>","DOI":"10.1017\/s0960129512000758","type":"journal-article","created":{"date-parts":[[2014,4,1]],"date-time":"2014-04-01T09:44:40Z","timestamp":1396345480000},"source":"Crossref","is-referenced-by-count":5,"title":["Probability, statistics and computation in dynamical systems"],"prefix":"10.1017","volume":"24","author":[{"given":"STEFANO","family":"GALATOLO","sequence":"first","affiliation":[]},{"given":"ISAIA","family":"NISOLI","sequence":"additional","affiliation":[]},{"given":"CRIST\u00d3BAL","family":"ROJAS","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,28]]},"reference":[{"key":"S0960129512000758_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-006-1546-3"},{"key":"S0960129512000758_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2008.12.009"},{"key":"S0960129512000758_ref27","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1973-0335758-1"},{"key":"S0960129512000758_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4364-9"},{"key":"S0960129512000758_ref33","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5775-2"},{"key":"S0960129512000758_ref31","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-45335-0_14"},{"key":"S0960129512000758_ref30","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-70335-5"},{"key":"S0960129512000758_ref29","first-page":"78","article-title":"The measure of maximal entropy of a rational endomorphism of a Riemann sphere.","volume":"16","author":"Lyubich","year":"1982","journal-title":"Funktsional'nyi Analiz i ego prilozheniya"},{"key":"S0960129512000758_ref28","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/14\/3\/303"},{"key":"S0960129512000758_ref24","volume-title":"Introduction to the Modern Theory of Dynamical Systems","author":"Hasselblatt","year":"1995"},{"key":"S0960129512000758_ref22","doi-asserted-by":"crossref","first-page":"193","DOI":"10.3934\/dcds.2011.29.193","article-title":"Dynamics and abstract computability: computing invariant measures.","volume":"29","author":"Galatolo","year":"2011","journal-title":"Discrete and Continuous Dynamical Systems"},{"key":"S0960129512000758_ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2009.02.010"},{"key":"S0960129512000758_ref19","unstructured":"Galatolo S. and Nisoli I. (2012) A simple approach to rigorous approximation of invariant measures. arXiv:1109.2342"},{"key":"S0960129512000758_ref16","first-page":"221","volume-title":"Handbook of dynamical systems","author":"Dellnitz","year":"2002"},{"key":"S0960129512000758_ref12","doi-asserted-by":"crossref","unstructured":"Braverman M. , Grigo A. and Rojas C. (2012) Noise vs computational intractability in dynamics. arXiv:1201.0488.","DOI":"10.1145\/2090236.2090247"},{"key":"S0960129512000758_ref8","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/19\/6\/009"},{"key":"S0960129512000758_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02591353"},{"key":"S0960129512000758_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.entcs.2004.06.031"},{"key":"S0960129512000758_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01933190"},{"key":"S0960129512000758_ref23","first-page":"1","article-title":"Statistical properties of dynamical systems - simulation and abstract computation.","volume":"45","author":"Galatolo","year":"2011","journal-title":"Chaos, Solitons and Fractals"},{"key":"S0960129512000758_ref32","first-page":"230","article-title":"On computable numbers, with an application to the Entscheidungsproblem","volume":"42","author":"Turing","year":"1936","journal-title":"Proceedings of the London Mathematical Society"},{"key":"S0960129512000758_ref1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-09-04814-4"},{"key":"S0960129512000758_ref26","doi-asserted-by":"publisher","DOI":"10.1080\/10586458.1998.10504377"},{"key":"S0960129512000758_ref15","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142996313002"},{"key":"S0960129512000758_ref10","volume-title":"Computability of Julia sets, Algorithms and Computation in Mathematics","author":"Braverman","year":"2008"},{"key":"S0960129512000758_ref21","doi-asserted-by":"crossref","unstructured":"Galatolo S. , Hoyrup M. and Rojas C. (2010) Computing the speed of convergence of ergodic averages and pseudorandom points in computable dynamical systems. In: Proceedings 7th International Conference on Computability and Complexity in Analysis. arXiv.org\/abs\/1006.0392v1.","DOI":"10.4204\/EPTCS.24.6"},{"key":"S0960129512000758_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-68546-5_18"},{"key":"S0960129512000758_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-011-1363-1"},{"key":"S0960129512000758_ref35","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019762724717"},{"key":"S0960129512000758_ref17","first-page":"283","volume-title":"Proceedings Nonlinear Dynamics and Statistics: Newton Institute, Cambridge 1998","author":"Froyland","year":"2001"},{"key":"S0960129512000758_ref3","first-page":"405","article-title":"Filled Julia sets with empty interior are computable.","volume":"7","author":"Binder","year":"2007","journal-title":"Journal FoCM"},{"key":"S0960129512000758_ref34","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-56999-9","volume-title":"Computable Analysis. An Introduction","author":"Weihrauch","year":"2000"},{"key":"S0960129512000758_ref18","doi-asserted-by":"crossref","first-page":"203","DOI":"10.3934\/dcds.2007.17.671","article-title":"On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps.","volume":"17","author":"Froyland","year":"2007","journal-title":"Discrete and Continuous Dynamical Systems"},{"key":"S0960129512000758_ref11","doi-asserted-by":"crossref","first-page":"185","DOI":"10.17323\/1609-4514-2008-8-2-185-231","article-title":"Computability of Julia sets.","volume":"8","author":"Braverman","year":"2008","journal-title":"Moscow Mathematics Journal"},{"key":"S0960129512000758_ref9","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-05-00516-3"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129512000758","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,17]],"date-time":"2020-08-17T02:37:43Z","timestamp":1597631863000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129512000758\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,3,28]]},"references-count":35,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2014,6]]}},"alternative-id":["S0960129512000758"],"URL":"https:\/\/doi.org\/10.1017\/s0960129512000758","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,3,28]]},"article-number":"e240304"}}