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Despite many interesting and non-trivial developments, only the case of conformal dynamics is completely understood. The study of the dimension of invariant sets of non-conformal maps has unveiled several new phenomena, but it still lacks today a satisfactory general approach. Indeed, we have a complete understanding of only a few classes of invariant sets of non-conformal maps satisfying certain simplifying assumptions. For example, the assumptions may ensure that there is a clear separation between different Lyapunov directions or that number-theoretical properties do not influence the dimension.<\/jats:p>","DOI":"10.1017\/s014338571000012x","type":"journal-article","created":{"date-parts":[[2010,5,26]],"date-time":"2010-05-26T08:47:39Z","timestamp":1274863659000},"page":"641-671","source":"Crossref","is-referenced-by-count":33,"title":["Dimension estimates in smooth dynamics: a survey of recent results"],"prefix":"10.1017","volume":"31","author":[{"given":"LUIS","family":"BARREIRA","sequence":"first","affiliation":[]},{"given":"KATRIN","family":"GELFERT","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2010,5,26]]},"reference":[{"key":"S014338571000012X_manual_ref-72","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0083071"},{"key":"S014338571000012X_manual_ref-73","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100072789"},{"key":"S014338571000012X_manual_ref-4","volume-title":"Dimension and Recurrence in Hyperbolic Dynamics","author":"Barreira","year":"2008"},{"key":"S014338571000012X_manual_ref-36","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385797060987"},{"key":"S014338571000012X_manual_ref-43","first-page":"331","volume-title":"Modern Dynamical Systems and Applications","author":"Hasselblatt","year":"2004"},{"key":"S014338571000012X_manual_ref-8","unstructured":"[8] Bedford, T. . 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