{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T09:18:38Z","timestamp":1775121518663,"version":"3.50.1"},"reference-count":23,"publisher":"Pleiades Publishing Ltd","issue":"4","license":[{"start":{"date-parts":[[2013,7,1]],"date-time":"2013-07-01T00:00:00Z","timestamp":1372636800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2013,7,1]],"date-time":"2013-07-01T00:00:00Z","timestamp":1372636800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Regul. Chaot. Dyn."],"published-print":{"date-parts":[[2013,7]]},"DOI":"10.1134\/s1560354713040072","type":"journal-article","created":{"date-parts":[[2013,8,6]],"date-time":"2013-08-06T07:23:07Z","timestamp":1375773787000},"page":"425-452","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Singular sets of planar hyperbolic billiards are regular"],"prefix":"10.1134","volume":"18","author":[{"given":"Gianluigi","family":"Del Magno","sequence":"first","affiliation":[]},{"given":"Roberto","family":"Markarian","sequence":"additional","affiliation":[]}],"member":"137","published-online":{"date-parts":[[2013,8,7]]},"reference":[{"issue":"15","key":"6237_CR1","first-page":"49","volume":"94136","author":"LA Bunimovich","year":"1974","unstructured":"Bunimovich, L.A., On Billiards Close to Dispersing, Mat. Sb., 1974, vol. 94(136), no. 1(5), pp. 49\u201373 [Sb. Math., 1974, vol. 23, no. 1, pp. 45\u201367].","journal-title":"Mat. Sb."},{"issue":"3","key":"6237_CR2","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1007\/BF01197884","volume":"65","author":"LA Bunimovich","year":"1979","unstructured":"Bunimovich, L.A., On the Ergodic Properties of Nowhere Dispersing Billiards, Comm. Math. Phys., 1979, vol. 65, no. 3, pp. 295\u2013312.","journal-title":"Comm. Math. Phys."},{"issue":"3","key":"6237_CR3","doi-asserted-by":"publisher","first-page":"599","DOI":"10.1007\/BF02096936","volume":"130","author":"LA Bunimovich","year":"1990","unstructured":"Bunimovich, L.A., A Theorem on Ergodicity of Two-Dimensional Hyperbolic Billiards, Comm. Math. Phys., 1990, vol. 130, no. 3, pp. 599\u2013621.","journal-title":"Comm. Math. Phys."},{"key":"6237_CR4","series-title":"Lecture Notes in Math.","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1007\/BFb0097528","volume-title":"Ergodic Theory and Related Topics, III (G\u00fcstrow, 1990)","author":"LA Bunimovich","year":"1992","unstructured":"Bunimovich, L.A., On Absolutely Focusing Mirrors, in Ergodic Theory and Related Topics, III (G\u00fcstrow, 1990), Lecture Notes in Math., vol. 1514, Berlin: Springer, 1992, pp. 62\u201382."},{"issue":"2","key":"6237_CR5","doi-asserted-by":"publisher","first-page":"699","DOI":"10.1007\/s00220-009-0741-4","volume":"288","author":"LA Bunimovich","year":"2009","unstructured":"Bunimovich, L.A. and Del Magno, G., Track Billiards, Comm. Math. Phys., 2009, vol. 288, no. 2, pp. 699\u2013713.","journal-title":"Comm. Math. Phys."},{"issue":"18","key":"6237_CR6","doi-asserted-by":"publisher","first-page":"2272","DOI":"10.1016\/j.physd.2008.02.006","volume":"237","author":"L Bussolari","year":"2008","unstructured":"Bussolari, L. and Lenci, M., Hyperbolic Billiards with Nearly Flat Focusing Boundaries: 1, Phys. D, 2008, vol. 237, no. 18, pp. 2272\u20132281.","journal-title":"Phys. D"},{"key":"6237_CR7","series-title":"Math. Surveys Monogr.","doi-asserted-by":"crossref","DOI":"10.1090\/surv\/127","volume-title":"Chaotic Billiards","author":"N Chernov","year":"2006","unstructured":"Chernov, N. and Markarian, R., Chaotic Billiards, Math. Surveys Monogr., vol. 127, Providence, RI: AMS, 2006."},{"issue":"3","key":"6237_CR8","doi-asserted-by":"publisher","first-page":"727","DOI":"10.1007\/s00220-006-0169-z","volume":"270","author":"N Chernov","year":"2007","unstructured":"Chernov, N. and Markarian, R., Dispersing Billiards with Cusps: Slow Decay of Correlations, Comm. Math. Phys., 2007, vol. 270, no. 3, pp. 727\u2013758.","journal-title":"Comm. Math. Phys."},{"issue":"4","key":"6237_CR9","doi-asserted-by":"publisher","first-page":"1095","DOI":"10.1088\/0951-7715\/11\/4\/019","volume":"11","author":"N Chernov","year":"1998","unstructured":"Chernov, N. and Troubetzkoy, S., Ergodicity of Billiards in Polygons with Pockets, Nonlinearity, 1998, vol. 11, no. 4, pp. 1095\u20131102.","journal-title":"Nonlinearity"},{"issue":"6","key":"6237_CR10","doi-asserted-by":"publisher","first-page":"1761","DOI":"10.1088\/0951-7715\/14\/6\/317","volume":"14","author":"G Del Magno","year":"2001","unstructured":"Del Magno, G., Ergodicity of a Class of Truncated Elliptical Billiards, Nonlinearity, 2001, vol. 14, no. 6, pp. 1761\u20131786.","journal-title":"Nonlinearity"},{"issue":"2","key":"6237_CR11","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s00220-002-0752-x","volume":"233","author":"G Del Magno","year":"2003","unstructured":"Del Magno, G. and Markarian, R., Bernoulli Elliptical Stadia, Comm. Math. Phys., 2003, vol. 233, no. 2, pp. 211\u2013230.","journal-title":"Comm. Math. Phys."},{"issue":"4","key":"6237_CR12","doi-asserted-by":"publisher","first-page":"983","DOI":"10.1017\/S0143385712000284","volume":"33","author":"G Del Magno","year":"2013","unstructured":"Del Magno, G. and Markarian, R., A Local Ergodic Theorem Non-Uniformly Hyperbolic Symplectic Maps with Singularities, Ergodic Theory Dynam. Systems, 2013, vol. 33, no. 4, pp. 983\u20131007.","journal-title":"Ergodic Theory Dynam. Systems"},{"issue":"2","key":"6237_CR13","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/BF02101504","volume":"141","author":"V J Donnay","year":"1991","unstructured":"Donnay, V. J., Using Integrability to Produce Chaos: Billiards with Positive Entropy, Comm. Math. Phys., 1991, vol. 141, no. 2, pp. 225\u2013257.","journal-title":"Comm. Math. Phys."},{"key":"6237_CR14","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/BF01651505","volume":"38","author":"G Gallavotti","year":"1974","unstructured":"Gallavotti, G. and Ornstein, D. S., Billiards and Bernoulli Schemes, Comm. Math. Phys., 1974, vol. 38, pp. 83\u2013101.","journal-title":"Comm. Math. Phys."},{"key":"6237_CR15","first-page":"261","volume":"91","author":"E Hopf","year":"1939","unstructured":"Hopf, E., Statistik der geod\u00e4tischen Linien inMannigfaltigkeiten negativer Kr\u00fcmmung, Ber. Verh. S\u00e4chs. Akad. Wiss. Leipzig, 1939, vol. 91, pp. 261\u2013304.","journal-title":"Ber. Verh. S\u00e4chs. Akad. Wiss. Leipzig"},{"key":"6237_CR16","series-title":"Lecture Notes in Math.","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0099031","volume-title":"Invariant Manifolds, Entropy and Billiards; Smooth Maps with Singularities","author":"A Katok","year":"1986","unstructured":"Katok, A., Strelcyn, J.-M., Ledrappier, F., and Przytycki, F., Invariant Manifolds, Entropy and Billiards; Smooth Maps with Singularities, Lecture Notes in Math., vol. 1222, Berlin: Springer, 1986."},{"key":"6237_CR17","volume-title":"Ergeb. Math. Grenzgeb. (3)","author":"V F Lazutkin","year":"1993","unstructured":"Lazutkin, V. F., KAM Theory and Semiclassical Approximations to Eigenfunctions, Ergeb. Math. Grenzgeb. (3), vol. 24, Berlin: Springer, 1993."},{"key":"6237_CR18","first-page":"130","volume-title":"Expositions Dynam. Systems (N. S.), vol. 4","author":"C Liverani","year":"1995","unstructured":"Liverani, C. and Wojtkowski, M.P., Ergodicity in Hamiltonian Systems, in Dynamics Reported, Dynam. Report. Expositions Dynam. Systems (N. S.), vol. 4, Berlin: Springer, 1995, pp. 130\u2013202."},{"issue":"1","key":"6237_CR19","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1007\/BF01218478","volume":"118","author":"R Markarian","year":"1988","unstructured":"Markarian, R., Billiards with Pesin Region of Measure One, Comm. Math. Phys., 1988, vol. 118, no. 1, pp. 87\u201397.","journal-title":"Comm. Math. Phys."},{"issue":"5","key":"6237_CR20","doi-asserted-by":"publisher","first-page":"819","DOI":"10.1088\/0951-7715\/6\/5\/009","volume":"6","author":"R Markarian","year":"1993","unstructured":"Markarian, R., New Ergodic Billiards: Exact Results, Nonlinearity, 1993, vol. 6, no. 5, pp. 819\u2013841.","journal-title":"Nonlinearity"},{"issue":"2","key":"6237_CR21","first-page":"141","volume":"25","author":"YaG Sinai","year":"1970","unstructured":"Sinai, Ya.G., Dynamical Systems with Elastic Reflections. Ergodic Properties of Dispersing Billiards, Uspekhi Mat. Nauk, 1970, vol. 25, no. 2, pp. 141\u2013192 [Russian Math. Surveys, 1970, vol. 25, no. 2, pp. 137\u2013189].","journal-title":"Uspekhi Mat. Nauk"},{"issue":"3","key":"6237_CR22","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1007\/BF02099399","volume":"145","author":"D Sz\u00e1sz","year":"1992","unstructured":"Sz\u00e1sz, D., On the K-Property of Some Planar Hyperbolic Billiards, Comm. Math. Phys., 1992, vol. 145, no. 3, pp. 595\u2013604.","journal-title":"Comm. Math. Phys."},{"issue":"3","key":"6237_CR23","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1007\/BF01205934","volume":"105","author":"M Wojtkowski","year":"1986","unstructured":"Wojtkowski, M., Principles for the Design of Billiards with Nonvanishing Lyapunov Exponents, Comm. Math. Phys., 1986, vol. 105, no. 3, pp. 391\u2013414.","journal-title":"Comm. Math. Phys."}],"container-title":["Regular and Chaotic Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S1560354713040072.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1134\/S1560354713040072","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1134\/S1560354713040072","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S1560354713040072.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T19:52:30Z","timestamp":1775073150000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1134\/S1560354713040072"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,7]]},"references-count":23,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2013,7]]}},"alternative-id":["6237"],"URL":"https:\/\/doi.org\/10.1134\/s1560354713040072","relation":{},"ISSN":["1560-3547","1468-4845"],"issn-type":[{"value":"1560-3547","type":"print"},{"value":"1468-4845","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,7]]},"assertion":[{"value":"26 November 2012","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 May 2013","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 August 2013","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}