{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T18:19:53Z","timestamp":1725560393567},"publisher-location":"Berlin, Heidelberg","reference-count":27,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540287025"},{"type":"electronic","value":"9783540318675"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2005]]},"DOI":"10.1007\/11549345_65","type":"book-chapter","created":{"date-parts":[[2005,9,27]],"date-time":"2005-09-27T10:05:47Z","timestamp":1127815547000},"page":"757-768","source":"Crossref","is-referenced-by-count":1,"title":["On Beta-Shifts Having Arithmetical Languages"],"prefix":"10.1007","author":[{"given":"Jakob Grue","family":"Simonsen","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"65_CR1","volume-title":"Fractals Everywhere","author":"M.F. Barnsley","year":"1993","unstructured":"Barnsley, M.F.: Fractals Everywhere. Morgan Kaufmann, San Francisco (1993)"},{"key":"65_CR2","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/0304-3975(89)90038-8","volume":"65","author":"F. Blanchard","year":"1989","unstructured":"Blanchard, F.: \u03b2-Expansions and Symbolic Dynamics. Theoretical Computer Science\u00a065, 131\u2013141 (1989)","journal-title":"Theoretical Computer Science"},{"key":"65_CR3","volume-title":"Graduate Texts in Mathematics","author":"D.S. Bridges","year":"1994","unstructured":"Bridges, D.S.: Computability: A Mathematical Sketchbook. In: Graduate Texts in Mathematics, vol.\u00a0146, Springer, Heidelberg (1994)"},{"key":"65_CR4","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1016\/j.tcs.2004.02.018","volume":"319","author":"J.-C. Delvenne","year":"2004","unstructured":"Delvenne, J.-C., Blondel, V.D.: Quasi-Periodic Configurations and Undecidable Dynamics for Tilings, Infinite Words and Turing Machines. Theoretical Computer Science\u00a0319, 127\u2013143 (2004)","journal-title":"Theoretical Computer Science"},{"key":"65_CR5","doi-asserted-by":"publisher","first-page":"713","DOI":"10.1017\/S0143385700007057","volume":"12","author":"C. Frougny","year":"1992","unstructured":"Frougny, C., Solomyak, B.: Finite Beta-Expansions. Ergodic Theory and Dynamical Systems\u00a012, 713\u2013723 (1992)","journal-title":"Ergodic Theory and Dynamical Systems"},{"key":"65_CR6","series-title":"Lecture Notes in Computer Science","first-page":"515","volume-title":"STACS 1992","author":"G. Hansel","year":"1992","unstructured":"Hansel, G., Perrin, D., Simon, I.: Compression and Entropy. In: Finkel, A., Jantzen, M. (eds.) STACS 1992. LNCS, vol.\u00a0577, pp. 515\u2013528. Springer, Heidelberg (1992)"},{"key":"65_CR7","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/BF01534862","volume":"85","author":"F. Hofbauer","year":"1978","unstructured":"Hofbauer, F.: \u03b2-Shifts have Unique Maximal Measure. Monatshefte f\u00fcr Mathematik\u00a085, 189\u2013198 (1978)","journal-title":"Monatshefte f\u00fcr Mathematik"},{"key":"65_CR8","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1017\/S0143385700006738","volume":"12","author":"L. Hurd","year":"1992","unstructured":"Hurd, L., Kari, J., Culik, K.: The Topological Entropy of Cellular Automata is Uncomputable. Ergodic Theory and Dynamical Systems\u00a012, 255\u2013265 (1992)","journal-title":"Ergodic Theory and Dynamical Systems"},{"issue":"2","key":"65_CR9","first-page":"351","volume":"4","author":"P. Koiran","year":"2001","unstructured":"Koiran, P.: The Topological Entropy of Iterated Piecewise Affine Maps is Uncomputable. Discrete Mathematics and Theoretical Computer Science\u00a04(2), 351\u2013356 (2001)","journal-title":"Discrete Mathematics and Theoretical Computer Science"},{"key":"65_CR10","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1017\/S0143385700002443","volume":"4","author":"D. Lind","year":"1984","unstructured":"Lind, D.: The Entropies of Topological Markov Shifts and a Related Class of Algebraic Integers. Ergodic Theory and Dynamical Systems\u00a04, 283\u2013300 (1984)","journal-title":"Ergodic Theory and Dynamical Systems"},{"key":"65_CR11","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511626302","volume-title":"An Introduction to Symbolic Dynamics and Coding","author":"D. Lind","year":"1995","unstructured":"Lind, D., Marcus, B.: An Introduction to Symbolic Dynamics and Coding. cambridge University Press, Cambridge (1995)"},{"key":"65_CR12","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1090\/S0002-9947-1921-1501161-8","volume":"22","author":"M. Morse","year":"1921","unstructured":"Morse, M.: Recurrent Geodesics on a Surface of Negative Curvature. Transactions of the American Mathematical Society\u00a022, 84\u2013110 (1921)","journal-title":"Transactions of the American Mathematical Society"},{"key":"65_CR13","doi-asserted-by":"publisher","first-page":"7","DOI":"10.2307\/2266321","volume":"18","author":"J. Myhill","year":"1953","unstructured":"Myhill, J.: Criteria of Constructivity for Real Numbers. Journal of Symbolic Logic\u00a018, 7\u201310 (1953)","journal-title":"Journal of Symbolic Logic"},{"key":"65_CR14","series-title":"Studies of Logic and the Foundations of Mathematics","volume-title":"Classical Recursion Theory","author":"P. Odifreddi","year":"1989","unstructured":"Odifreddi, P.: Classical Recursion Theory. Studies of Logic and the Foundations of Mathematics, vol.\u00a0129. North-Holland, Amsterdam (1989)"},{"key":"65_CR15","doi-asserted-by":"crossref","unstructured":"Parry, W.: On the \u03b2-Expansion of Real Numbers. In: Acta Math. Acad. Sci. Hung, pp. 401\u2013416 (1960)","DOI":"10.1007\/BF02020954"},{"key":"65_CR16","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1007\/BF02020331","volume":"8","author":"A. Renyi","year":"1957","unstructured":"Renyi, A.: Representations for Real Numbers and their Ergodic Properties. Acta Math. Acad. Sci. Hung.\u00a08, 477\u2013493 (1957)","journal-title":"Acta Math. Acad. Sci. Hung."},{"key":"65_CR17","doi-asserted-by":"publisher","first-page":"784","DOI":"10.1090\/S0002-9939-1954-0063328-5","volume":"5","author":"H.G. Rice","year":"1954","unstructured":"Rice, H.G.: Recursive Real Numbers. Proceedings of the American Mathematical Society\u00a05, 784\u2013791 (1954)","journal-title":"Proceedings of the American Mathematical Society"},{"key":"65_CR18","series-title":"paperback edition","volume-title":"Theory of Recursive Functions and Effective Computability","author":"H. Rogers Jr.","year":"1987","unstructured":"Rogers Jr., H.: Theory of Recursive Functions and Effective Computability. paperback edition. The MIT Press, Cambridge (1987)"},{"key":"65_CR19","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1112\/blms\/12.4.269","volume":"12","author":"K. Schmidt","year":"1980","unstructured":"Schmidt, K.: On Periodic Expansions of Pisot Numbers and Salem Numbers. Bulletin of the London Mathematical Society\u00a012, 269\u2013278 (1980)","journal-title":"Bulletin of the London Mathematical Society"},{"key":"65_CR20","doi-asserted-by":"publisher","first-page":"838","DOI":"10.2307\/3647804","volume":"110","author":"N. Sidorov","year":"2003","unstructured":"Sidorov, N.: Almost Every Number has a Continuum of Beta-Expansions. American Mathematic Monthly\u00a0110, 838\u2013842 (2003)","journal-title":"American Mathematic Monthly"},{"key":"65_CR21","doi-asserted-by":"crossref","unstructured":"Sidorov, N.: Arithmetic Dynamics. In: Topics in Dynamics and Ergodic Theory. London Mathematical Society Lecture Notes Series, vol.\u00a0310, pp. 145\u2013189. London Mathematical Society (2003)","DOI":"10.1017\/CBO9780511546716.010"},{"key":"65_CR22","first-page":"599","volume":"20","author":"Y. Takahashi","year":"1983","unstructured":"Takahashi, Y.: Shift with Free Orbit Basis and Realization of One-Dimensional Maps. Osaka Journal of Mathematics\u00a020, 599\u2013629 (1983)","journal-title":"Osaka Journal of Mathematics"},{"issue":"2","key":"65_CR23","first-page":"230","volume":"42","author":"A.M. Turing","year":"1936","unstructured":"Turing, A.M.: On Computable Numbers with an Application to the, Entscheidungsproblem. Proceedings of the London Mathematical Society\u00a042(2), 230\u2013265 (1936)","journal-title":"Proceedings of the London Mathematical Society"},{"key":"65_CR24","volume-title":"Graduate Texts in Mathematics","author":"P. Walters","year":"1981","unstructured":"Walters, P.: An Introduction to Ergodic Theory. In: Graduate Texts in Mathematics, vol.\u00a079, Springer, Heidelberg (1981)"},{"key":"65_CR25","volume-title":"Computable Analysis: An Introduction","author":"K. Weihrauch","year":"1998","unstructured":"Weihrauch, K.: Computable Analysis: An Introduction. Springer, Heidelberg (1998)"},{"key":"65_CR26","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1002\/1521-3870(200210)48:1+<131::AID-MALQ131>3.0.CO;2-#","volume":"48","author":"X. Zheng","year":"2002","unstructured":"Zheng, X.: Recursive Approximability of Real Numbers. Mathematical Logic Quarterly\u00a048, 131\u2013156 (2002)","journal-title":"Mathematical Logic Quarterly"},{"issue":"1","key":"65_CR27","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1002\/1521-3870(200101)47:1<51::AID-MALQ51>3.0.CO;2-W","volume":"47","author":"X. Zheng","year":"2001","unstructured":"Zheng, X., Weihrauch, K.: The Arithmetical Hierarchy of Real Numbers. Mathematical Logic Quarterly\u00a047(1), 51\u201365 (2001)","journal-title":"Mathematical Logic Quarterly"}],"container-title":["Lecture Notes in Computer Science","Mathematical Foundations of Computer Science 2005"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/11549345_65.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T14:41:22Z","timestamp":1605624082000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/11549345_65"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005]]},"ISBN":["9783540287025","9783540318675"],"references-count":27,"URL":"https:\/\/doi.org\/10.1007\/11549345_65","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2005]]}}}