{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,20]],"date-time":"2024-06-20T09:07:52Z","timestamp":1718874472350},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,1,11]],"date-time":"2016-01-11T00:00:00Z","timestamp":1452470400000},"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":["J Geom Anal"],"published-print":{"date-parts":[[2017,1]]},"DOI":"10.1007\/s12220-015-9671-x","type":"journal-article","created":{"date-parts":[[2016,1,11]],"date-time":"2016-01-11T15:54:50Z","timestamp":1452527690000},"page":"1-55","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Discrete Orbits, Recurrence and Solvable Subgroups of $${{\\mathrm{Diff}}\\, ({{\\mathbb {C}}}^2, 0)}$$ Diff ( C 2 , 0 )"],"prefix":"10.1007","volume":"27","author":[{"given":"Julio C.","family":"Rebelo","sequence":"first","affiliation":[]},{"given":"Helena","family":"Reis","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,1,11]]},"reference":[{"issue":"1","key":"9671_CR1","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1215\/S0012-7094-01-10719-9","volume":"107","author":"M Abate","year":"2001","unstructured":"Abate, M.: The residual index and the dynamics of holomorphic maps tangent to the identity. Duke Math. J. 107(1), 173\u2013207 (2001)","journal-title":"Duke Math. J."},{"key":"9671_CR2","volume-title":"Discrete Groups in Space and Uniformization Problems, Mathematics and its Applications","author":"B Apanasov","year":"1991","unstructured":"Apanasov, B.: Discrete Groups in Space and Uniformization Problems, Mathematics and its Applications. Kluwer Academic Publishers, Dordrecht (1991)"},{"key":"9671_CR3","doi-asserted-by":"crossref","unstructured":"Arizzi, M., Raissy, J.: On Ecalle\u2013Hakim\u2019s theorem in holomorphic dynamics, frontiers in complex dynamics. In: Celebration of John Milnor\u2019s 80th birthday pp. 387\u2013449 (2014)","DOI":"10.1515\/9781400851317-017"},{"key":"9671_CR4","unstructured":"Camacho, C.: Problems on limit set of foliations on complex projective spaces. In: Proceedings of ICM, Vol I, II, (Kyoto 1990) Math. Soc. Japan, Tokyo pp. 1235\u20131239 (1991)"},{"key":"9671_CR5","first-page":"57","volume":"261","author":"C Camacho","year":"2000","unstructured":"Camacho, C., Scardua, B.: Complex foliations with algebraic limit sets. Ast\u00e9risque 261, 57\u201388 (2000)","journal-title":"Ast\u00e9risque"},{"key":"9671_CR6","first-page":"129","volume":"29","author":"P Harpe de la","year":"1983","unstructured":"de la Harpe, P.: Free groups in linear groups. L\u2019Enseignement Math. 29, 129\u2013144 (1983)","journal-title":"L\u2019Enseignement Math."},{"key":"9671_CR7","unstructured":"\u00c9calle, J.: Les fonctions r\u00e9surgentes. Publ. Math. Orsay 81\u201305 (1981)"},{"key":"9671_CR8","first-page":"57","volume":"14","author":"P Elizarov","year":"1993","unstructured":"Elizarov, P., Il\u2019yashenko, Y., Shcherbakov, A., Voronin, S.: Finitely generated groups of germs of one-dimensional conformal mappings and invariants for complex singular points of analytic foliations of the complex plane. Adv. Sov. Math. 14, 57\u2013105 (1993)","journal-title":"Adv. Sov. Math."},{"key":"9671_CR9","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/BFb0078013","volume-title":"Analyse harmonique sur les groupes de Lie \u2013 S\u00e9minaire Nancy-Strasbourg","author":"P Eymard","year":"1975","unstructured":"Eymard, P.: Initiation \u00e0 la th\u00e9orie des groupes moyennables. Analyse harmonique sur les groupes de Lie \u2013 S\u00e9minaire Nancy-Strasbourg. Lecture Notes in Mathematics, vol. 497, pp. 89\u2013107. Springer, New York (1975)"},{"key":"9671_CR10","volume-title":"Automorphic Functions","author":"L Ford","year":"1951","unstructured":"Ford, L.: Automorphic Functions, 2nd edn. Chelsea Publishing Co., New York (1951)","edition":"2"},{"issue":"2","key":"9671_CR11","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/BF01237675","volume":"24","author":"E Ghys","year":"1993","unstructured":"Ghys, E.: Sur les groupes engendr\u00e9s par les diff\u00e9omorphismes proches de l\u2019identit\u00e9. Bol. Soc. Bras. Mat. 24(2), 137\u2013178 (1993)","journal-title":"Bol. Soc. Bras. Mat."},{"issue":"2","key":"9671_CR12","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1215\/S0012-7094-98-09212-2","volume":"92","author":"M Hakim","year":"1998","unstructured":"Hakim, M.: Analytic transformations of $$(\\mathbb{C}^p, 0)$$ ( C p , 0 ) tangent to the identity. Duke Math. J. 92(2), 403\u2013428 (1998)","journal-title":"Duke Math. J."},{"key":"9671_CR13","volume-title":"Lectures on the Icosahedron","author":"F Klein","year":"2003","unstructured":"Klein, F.: Lectures on the Icosahedron. Dover Publications, New York (2003)"},{"key":"9671_CR14","unstructured":"Loray, F.: Pseudo-groupe d\u2019une singularit\u00e9 de feuilletage holomorphe en dimension deux, available from hal.archives-ouvertes.fr\/hal-00016434, (2005)"},{"key":"9671_CR15","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/s10097-002-0049-6","volume":"5","author":"F Loray","year":"2003","unstructured":"Loray, F., Rebelo, J.C.: Minimal, rigid foliations by curves in $$\\mathbb{C} {\\mathbb{P}}^n$$ C P n . J. Eur. Math. Soc. 5, 147\u2013201 (2003)","journal-title":"J. Eur. Math. Soc."},{"issue":"3\u20134","key":"9671_CR16","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1007\/s00208-013-0975-5","volume":"358","author":"M Martelo","year":"2014","unstructured":"Martelo, M., Ribon, J.: Derived length of solvable groups of local diffeomorphisms. Math. Ann. 358(3\u20134), 701\u2013728 (2014)","journal-title":"Math. Ann."},{"issue":"4","key":"9671_CR17","first-page":"469","volume":"13","author":"J-F Mattei","year":"1980","unstructured":"Mattei, J.-F., Moussu, R.: Holonomie et int\u00e9grales premi\u00e8res. Ann. Sci. E. N. S. S\u00e9rie IV 13(4), 469\u2013523 (1980)","journal-title":"Ann. Sci. E. N. S. S\u00e9rie IV"},{"issue":"8","key":"9671_CR18","doi-asserted-by":"crossref","first-page":"1401","DOI":"10.1112\/S0010437X13007161","volume":"149","author":"J-F Mattei","year":"2013","unstructured":"Mattei, J.-F., Rebelo, J.C., Reis, H.: Generic pseudogroups on $$(\\mathbb{C},0)$$ ( C , 0 ) and the topology of leaves. Compos. Math. 149(8), 1401\u20131430 (2013)","journal-title":"Compos. Math."},{"issue":"1","key":"9671_CR19","doi-asserted-by":"crossref","first-page":"33","DOI":"10.4310\/MAA.2001.v8.n1.a3","volume":"8","author":"JJ Morales-Ruiz","year":"2001","unstructured":"Morales-Ruiz, J.J., Ramis, J.P.: Ramis, Galoisian obstructions to integrability of Hamiltonian systems, I, II. Methods Appl. Anal. 8(1), 33\u201395 (2001)","journal-title":"Methods Appl. Anal."},{"issue":"6","key":"9671_CR20","first-page":"845","volume":"40","author":"JJ Morales-Ruiz","year":"2007","unstructured":"Morales-Ruiz, J.J., Ramis, J.-P., Sim\u00f3, C.: Integrability of Hamiltonian systems and differential Galois groups of higher variational equations. Ann. Sci. E. N. S. S\u00e9rie IV 40(6), 845\u2013884 (2007)","journal-title":"Ann. Sci. E. N. S. S\u00e9rie IV"},{"issue":"2","key":"9671_CR21","doi-asserted-by":"crossref","first-page":"569","DOI":"10.5802\/aif.1410","volume":"44","author":"I Nakai","year":"1994","unstructured":"Nakai, I.: Separatrices for non solvable dynamics on $$(\\mathbb{C}, 0)$$ ( C , 0 ) . Ann. Inst. Fourier 44(2), 569\u2013599 (1994)","journal-title":"Ann. Inst. Fourier"},{"issue":"2","key":"9671_CR22","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1112\/jlms\/jdt069","volume":"89","author":"S Pinheiro","year":"2014","unstructured":"Pinheiro, S., Reis, H.: Topological aspects of completely integrable foliations. J. Lond. Math. Soc. 89(2), 415\u2013433 (2014)","journal-title":"J. Lond. Math. Soc."},{"issue":"2","key":"9671_CR23","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1017\/S1474748013000248","volume":"13","author":"JC Rebelo","year":"2014","unstructured":"Rebelo, J.C., Reis, H.: Cyclic stabilizers and infinitely many hyperbolic orbits for pseudogroups on $$(\\mathbb{C},0)$$ ( C , 0 ) . J. Inst. Math. Jussieu 13(2), 413\u2013446 (2014)","journal-title":"J. Inst. Math. Jussieu"},{"key":"9671_CR24","doi-asserted-by":"crossref","unstructured":"Rebelo, J.C., Reis, H.: A note on integrability and finite orbits for subgroups $${{\\rm Diff}}\\, (\\mathbb{C}^n,0)$$ Diff ( C n , 0 ) . Bull. Braz. Math. Soc. 46(3), 469\u2013490 (2015)","DOI":"10.1007\/s00574-015-0101-2"},{"key":"9671_CR25","unstructured":"Rebelo, J.C., Reis, H.: Discrete orbits and special subgroups $${\\rm Diff}\\,(\\mathbb{C}^n,0)$$ Diff ( C n , 0 ) , available from arXiv:1301.3716"},{"key":"9671_CR26","unstructured":"Rebelo, J.C., Reis, H.: Discrete orbits, recurrence and solvable subgroups of $${{\\rm Diff}}\\, (\\mathbb{C}^2,0)$$ Diff ( C 2 , 0 ) , available from arXiv:1406.0461"},{"key":"9671_CR27","unstructured":"Ribon, J.: Recurrent orbits of subgroups of local complex analytic diffeomorphisms, available from arXiv:1509.01153"},{"key":"9671_CR28","series-title":"Lectures Notes in Math 1500","volume-title":"Lie Algebras and Lie Groups: 1964 Lectures Given at Harvard University","author":"J-P Serre","year":"2009","unstructured":"Serre, J.-P.: Lie Algebras and Lie Groups: 1964 Lectures Given at Harvard University. Lectures Notes in Math 1500. Springer, Berlin (2009)"},{"issue":"4","key":"9671_CR29","first-page":"10","volume":"31","author":"A Shcherbakov","year":"1982","unstructured":"Shcherbakov, A.: On the density of an orbit of a pseudogroup of conformal mappings and a generalization of the Hudai-Verenov theorem. Vestnik Moskov Univ. Math. 31(4), 10\u201315 (1982)","journal-title":"Vestnik Moskov Univ. Math."},{"key":"9671_CR30","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/0021-8693(72)90058-0","volume":"20","author":"J Tits","year":"1972","unstructured":"Tits, J.: Free subgroups in linear groups. J. Algebra 20, 25\u2013270 (1972)","journal-title":"J. Algebra"},{"key":"9671_CR31","unstructured":"Wehrfritz, B.: Infinite linear groups, Erg. der Mathematik (1976)"},{"key":"9671_CR32","unstructured":"Yoccoz J.-C., Petits diviseurs en dimension $$1$$ 1 . Ast\u00e9risque, 231 (1995)"}],"container-title":["The Journal of Geometric Analysis"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12220-015-9671-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12220-015-9671-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12220-015-9671-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12220-015-9671-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T10:06:31Z","timestamp":1654077991000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12220-015-9671-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,11]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["9671"],"URL":"https:\/\/doi.org\/10.1007\/s12220-015-9671-x","relation":{},"ISSN":["1050-6926","1559-002X"],"issn-type":[{"value":"1050-6926","type":"print"},{"value":"1559-002X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1,11]]}}}