{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T06:13:13Z","timestamp":1725516793349},"publisher-location":"Berlin, Heidelberg","reference-count":34,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540697329"},{"type":"electronic","value":"9783540697336"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/978-3-540-69733-6_22","type":"book-chapter","created":{"date-parts":[[2008,8,12]],"date-time":"2008-08-12T12:07:43Z","timestamp":1218542863000},"page":"215-224","source":"Crossref","is-referenced-by-count":2,"title":["Dimensions of Points in Self-similar Fractals"],"prefix":"10.1007","author":[{"given":"Jack H.","family":"Lutz","sequence":"first","affiliation":[]},{"given":"Elvira","family":"Mayordomo","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"22_CR1","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1137\/S0097539703446912","volume":"37","author":"K.B. Athreya","year":"2007","unstructured":"Athreya, K.B., Hitchcock, J.M., Lutz, J.H., Mayordomo, E.: Effective Strong Dimension in Algorithmic Information and Computational Complexity. SIAM Journal on Computing\u00a037, 671\u2013705 (2007)","journal-title":"SIAM Journal on Computing"},{"key":"22_CR2","volume-title":"Fractals Everywhere","author":"M.F. Barnsley","year":"1993","unstructured":"Barnsley, M.F.: Fractals Everywhere. Morgan Kaufmann Pub., San Francisco (1993)"},{"key":"22_CR3","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1215\/ijm\/1255455863","volume":"4","author":"P. Billingsley","year":"1960","unstructured":"Billingsley, P.: Hausdorff Dimension in Probability Theory. Illinois J. Math\u00a04, 187\u2013209 (1960)","journal-title":"Illinois J. Math"},{"key":"22_CR4","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/S0304-3975(98)00284-9","volume":"219","author":"V. Brattka","year":"1999","unstructured":"Brattka, V., Weihrauch, K.: Computability on Subsets of Euclidean Space i: Closed and Compact Subsets. Theoretical Computer Science\u00a0219, 65\u201393 (1999)","journal-title":"Theoretical Computer Science"},{"key":"22_CR5","doi-asserted-by":"crossref","unstructured":"Braverman, M.: On the Complexity of Real Functions. In: Proceedings of the Forty-Sixth Annual IEEE Symposium on Foundations of Computer Science (FOCS 2005), pp. 155\u2013164 (2005)","DOI":"10.1109\/SFCS.2005.58"},{"issue":"3","key":"22_CR6","first-page":"1024","volume":"53","author":"M. Braverman","year":"2006","unstructured":"Braverman, M., Cook, S.: Computing over the Reals: Foundations for Scientific Computing. Notices of the AMS\u00a053(3), 1024\u20131034 (2006)","journal-title":"Notices of the AMS"},{"key":"22_CR7","doi-asserted-by":"crossref","unstructured":"Braverman, M., Yampolsky, M.: Constructing Non-computable Julia Sets. In: Proceedings of the Thirty-Ninth Annual ACM Symposium on Theory of Computing (STOC 2007), pp. 709\u2013716 (2007)","DOI":"10.1145\/1250790.1250893"},{"key":"22_CR8","doi-asserted-by":"publisher","first-page":"605","DOI":"10.1016\/S0022-0000(05)80073-X","volume":"49","author":"J. Cai","year":"1994","unstructured":"Cai, J., Hartmanis, J.: On Hausdorff and Topological Dimensions of the Kolmogorov Complexity of the Real Line. Journal of Computer and Systems Sciences\u00a049, 605\u2013619 (1994)","journal-title":"Journal of Computer and Systems Sciences"},{"key":"22_CR9","series-title":"Lecture Notes in Mathematics","volume-title":"Billingsley Dimension in Probability Spaces","author":"H. Cajar","year":"1982","unstructured":"Cajar, H.: Billingsley Dimension in Probability Spaces. Lecture Notes in Mathematics. Springer, Heidelberg (1982)"},{"key":"22_CR10","doi-asserted-by":"crossref","DOI":"10.1002\/0471200611","volume-title":"Elements of Information Theory","author":"T.M. Cover","year":"1991","unstructured":"Cover, T.M., Thomas, J.A.: Elements of Information Theory. John Wiley & Sons, Inc., New York (1991)"},{"key":"22_CR11","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2958-0","volume-title":"Integral, Probability, and Fractal Measures","author":"G.A. Edgar","year":"1998","unstructured":"Edgar, G.A.: Integral, Probability, and Fractal Measures. Springer, Heidelberg (1998)"},{"key":"22_CR12","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511623738","volume-title":"The Geometry of Fractal Sets","author":"K. Falconer","year":"1985","unstructured":"Falconer, K.: The Geometry of Fractal Sets. Cambridge University Press, Cambridge (1985)"},{"key":"22_CR13","doi-asserted-by":"publisher","first-page":"543","DOI":"10.2307\/2048840","volume":"106","author":"K. Falconer","year":"1989","unstructured":"Falconer, K.: Dimensions and Measures of Quasi Self-similar Sets. Proc. Amer. Math. Soc.\u00a0106, 543\u2013554 (1989)","journal-title":"Proc. Amer. Math. Soc."},{"key":"22_CR14","doi-asserted-by":"crossref","DOI":"10.1002\/0470013850","volume-title":"Fractal Geometry: Mathematical Foundations and Applications","author":"K. Falconer","year":"2003","unstructured":"Falconer, K.: Fractal Geometry: Mathematical Foundations and Applications. John Wiley & sons, Chichester (2003)"},{"key":"22_CR15","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1006\/inco.2000.2912","volume":"168","author":"H. Fernau","year":"2001","unstructured":"Fernau, H., Staiger, L.: Iterated Function Systems and Control Languages. Information and Computation\u00a0168, 125\u2013143 (2001)","journal-title":"Information and Computation"},{"key":"22_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/11672142_10","volume-title":"STACS 2006","author":"L. Fortnow","year":"2006","unstructured":"Fortnow, L., Lee, T., Vereshchagin, N.: Kolmogorov Complexity with Error. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol.\u00a03884, pp. 137\u2013148. Springer, Heidelberg (2006)"},{"key":"22_CR17","doi-asserted-by":"crossref","first-page":"168","DOI":"10.4064\/fm-42-1-168-202","volume":"42","author":"A. Grzegorczyk","year":"1955","unstructured":"Grzegorczyk, A.: Computable Functionals. Fundamenta Mathematicae\u00a042, 168\u2013202 (1955)","journal-title":"Fundamenta Mathematicae"},{"key":"22_CR18","doi-asserted-by":"crossref","unstructured":"Gu, X., Lutz, J.H., Mayordomo, E.: Points on Computable Curves. In: Proceedings of the Forty-Seventh Annual IEEE Symposium on Foundations of Computer Science (FOCS 2006), pp. 469\u2013474 (2006)","DOI":"10.1109\/FOCS.2006.63"},{"key":"22_CR19","doi-asserted-by":"crossref","unstructured":"Gupta, A., Krauthgamer, R., Lee, J.R.: Bounded Geometries, Fractals, and Low-Distortion Embeddings. In: Proceedings of the Forty-Fourth Annual IEEE Symposium on Foundations of Computer Science (FOCS 2003), pp. 534\u2013543 (2003)","DOI":"10.1109\/SFCS.2003.1238226"},{"key":"22_CR20","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1002\/malq.200310124","volume":"51","author":"P. Hertling","year":"2005","unstructured":"Hertling, P.: Is the Mandelbrot Set Computable? Mathematical Logic Quarterly\u00a051, 5\u201318 (2005)","journal-title":"Mathematical Logic Quarterly"},{"key":"22_CR21","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1007\/s00224-004-1122-1","volume":"38","author":"J.M. Hitchcock","year":"2005","unstructured":"Hitchcock, J.M.: Correspondence Principles for Effective Dimensions. Theory of Computing Systems\u00a038, 559\u2013571 (2005)","journal-title":"Theory of Computing Systems"},{"key":"22_CR22","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1002\/malq.19990450103","volume":"45","author":"H. Kamo","year":"1999","unstructured":"Kamo, H., Kawamura, K.: Computability of Self-Similar Sets. Math. Log. Q.\u00a045, 23\u201330 (1999)","journal-title":"Math. Log. Q."},{"key":"22_CR23","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-6802-1","volume-title":"Complexity Theory of Real Functions","author":"K. Ko","year":"1991","unstructured":"Ko, K.: Complexity Theory of Real Functions. Birkh\u00e4user, Boston (1991)"},{"key":"22_CR24","first-page":"2478","volume":"240","author":"D. Lacombe","year":"1955","unstructured":"Lacombe, D.: Extension de la Notion de Fonction Recursive aux Fonctions d\u2019une ow Plusiers Variables Reelles and other Notes. Comptes Rendus\u00a0240, 2478\u20132480; 241, 13\u201314; 151\u2013153, 1250\u20131252 (1955)","journal-title":"Comptes Rendus"},{"key":"22_CR25","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2606-0","volume-title":"An Introduction to Kolmogorov Complexity and its Applications","author":"M. Li","year":"1997","unstructured":"Li, M., Vit\u00e1nyi, P.M.B.: An Introduction to Kolmogorov Complexity and its Applications. 2nd edn. Springer, Berlin (1997)","edition":"2"},{"key":"22_CR26","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/S0890-5401(03)00187-1","volume":"187","author":"J.H. Lutz","year":"2003","unstructured":"Lutz, J.H.: The Dimensions of Individual Strings and Sequences. Information and Computation\u00a0187, 49\u201379 (2003)","journal-title":"Information and Computation"},{"key":"22_CR27","unstructured":"Lutz, J.H., Weihrauch, K.: Connectivity Properties of Dimension Level Sets. In: Proceedings of the Fourth International Conference on Computability and Complexity in Analysis (2007)"},{"key":"22_CR28","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1002\/malq.19660120125","volume":"12","author":"D.A. Martin","year":"1966","unstructured":"Martin, D.A.: Classes of Recursively Enumerable Sets and Degrees of Unsolvability. Zeitschrift f\u00fcr Mathematische Logik und Grundlagen der Mathematik 12, 295\u2013310 (1966)","journal-title":"Zeitschrift f\u00fcr Mathematische Logik und Grundlagen der Mathematik"},{"key":"22_CR29","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1017\/S0305004100022684","volume":"42","author":"P.A. Moran","year":"1946","unstructured":"Moran, P.A.: Additive Functions of Intervals and Hausdorff Dimension. Proceedings of the Cambridge Philosophical Society\u00a042, 5\u201323 (1946)","journal-title":"Proceedings of the Cambridge Philosophical Society"},{"key":"22_CR30","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-21717-7","volume-title":"Computability in Analysis and Physics","author":"M.B. Pour-El","year":"1989","unstructured":"Pour-El, M.B., Richards, J.I.: Computability in Analysis and Physics. Springer, Heidelberg (1989)"},{"key":"22_CR31","doi-asserted-by":"crossref","unstructured":"Rettinger, R., Weihrauch, K.: The Computational Complexity of some Julia Sets. In: Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing (SOTC 2003), pp. 177\u2013185 (2003)","DOI":"10.1145\/780542.780570"},{"key":"22_CR32","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1007\/s002240000086","volume":"31","author":"L. Staiger","year":"1998","unstructured":"Staiger, L.: A Tight Upper Bound on Kolmogorov Complexity and Uniformly Optimal prediction. Theory of Computing Systems\u00a031, 215\u2013229 (1998)","journal-title":"Theory of Computing Systems"},{"key":"22_CR33","doi-asserted-by":"crossref","unstructured":"Vereshchagin, K., Vitanyi, P.M.B.: Algorithmic Rate-Distortion Function. In: Proceedings IEEE Intn\u2019l Symp. Information Theory (2006)","DOI":"10.1109\/ISIT.2006.261723"},{"key":"22_CR34","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-56999-9","volume-title":"Computable Analysis. An Introduction","author":"K. Weihrauch","year":"2000","unstructured":"Weihrauch, K.: Computable Analysis. An Introduction. Springer, Heidelberg (2000)"}],"container-title":["Lecture Notes in Computer Science","Computing and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-69733-6_22.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,19]],"date-time":"2020-11-19T00:02:13Z","timestamp":1605744133000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-69733-6_22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540697329","9783540697336"],"references-count":34,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-69733-6_22","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[]}}