{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T21:02:10Z","timestamp":1648933330736},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2010,10,14]],"date-time":"2010-10-14T00:00:00Z","timestamp":1287014400000},"content-version":"unspecified","delay-in-days":5492,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ergod. Th. Dynam. Sys."],"published-print":{"date-parts":[[1995,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We classify the C<jats:sup>1+\u03b1<\/jats:sup> structures on embedded trees. This extends the results of Sullivan on embeddings of the binary tree to trees with arbitrary topology and to embeddings without bounded geometry and with contact points. We used these results in an earlier paper to describe the moduli spaces of smooth conjugacy classes of expanding maps and Markov maps on train tracks. In later papers we will use those results to do the same for pseudo-Anosov diffeomorphisms of surfaces. These results are also used in the classification of renormalisation limits of <jats:italic>C<\/jats:italic><jats:sup>1+\u03b1<\/jats:sup> diffeomorphisms of the circle.<\/jats:p>","DOI":"10.1017\/s014338570000972x","type":"journal-article","created":{"date-parts":[[2010,10,14]],"date-time":"2010-10-14T10:00:14Z","timestamp":1287050414000},"page":"969-992","source":"Crossref","is-referenced-by-count":7,"title":["Classifying C<sup>1<\/sup>+ structures on dynamical fractals: 2. Embedded trees"],"prefix":"10.1017","volume":"15","author":[{"given":"A. A.","family":"Pinto","sequence":"first","affiliation":[]},{"given":"D. A.","family":"Rand","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2010,10,14]]},"reference":[{"key":"S014338570000972X_ref008","first-page":"147","volume-title":"Workshop on dynamical systems. Papers in honour of Rene Thorn","author":"Rand","year":"1988"},{"key":"S014338570000972X_ref002","article-title":"Classifying C1+ structures on dynamical fractals: 1 The moduli space of solenoid functions for Markov maps on train tracks","volume":"15","author":"Pinto","year":"1995","journal-title":"Ergod. Th. and Dynam. Sys."},{"key":"S014338570000972X_ref010","first-page":"1216","volume-title":"Proc. Int. Congress of Mathematicians","author":"Sullivan","year":"1988"},{"key":"S014338570000972X_ref005","unstructured":"[5] Pinto A. A. . Convergence of renormalisation and rigidity of dynamical systems. Warwick PhD thesis 1991."},{"key":"S014338570000972X_ref003","unstructured":"[3] Pinto A. A. and Rand D. A. . The moduli space of horocycle C1+ smooth diffeomorphisms of the circle with bounded rotation number. In preparation."},{"key":"S014338570000972X_ref006","first-page":"1","volume-title":"New Directions in Dynamical Systems","author":"Rand","year":"1988"},{"key":"S014338570000972X_ref011","volume-title":"Amer. Math. Soc. Centennial Publications. Volume 2: Mathematics into the Twenty-first Century (1988 Centennial Symposium, August 8-12)","author":"Sullivan","year":"1991"},{"key":"S014338570000972X_ref007","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/1\/1\/007"},{"key":"S014338570000972X_ref009","volume-title":"Nonlinear evolution and Chaotic Phenomena","author":"Sullivan","year":"1988"},{"key":"S014338570000972X_ref001","first-page":"1","article-title":"Global phase space universality, smooth conjugacies and renormalisation: 2. The Ck+a case using rapid convergence of Markov families","volume":"4","author":"Pinto","year":"1991","journal-title":"Nonlinearity"},{"key":"S014338570000972X_ref004","unstructured":"[4] Pinto A. A. and Rand D. A. . Characterising flexibility and rigidity of pseudo-Anosov and other transversally laminated dynamical systems on surfaces. Warwick Preprint. 1995."}],"container-title":["Ergodic Theory and Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S014338570000972X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,13]],"date-time":"2019-05-13T20:37:34Z","timestamp":1557779854000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S014338570000972X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,10]]},"references-count":11,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1995,10]]}},"alternative-id":["S014338570000972X"],"URL":"https:\/\/doi.org\/10.1017\/s014338570000972x","relation":{},"ISSN":["0143-3857","1469-4417"],"issn-type":[{"value":"0143-3857","type":"print"},{"value":"1469-4417","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,10]]}}}