{"month":"12","author":[{"last_name":"Berger","first_name":"Pierre","full_name":"Berger, Pierre"},{"last_name":"Gourmelon","first_name":"Nicolaz","full_name":"Gourmelon, Nicolaz"},{"id":"7d296fbe-e2c6-11ee-84d3-d5c2945f9a57","full_name":"Helfter, Mathieu","first_name":"Mathieu","last_name":"Helfter"}],"OA_place":"repository","year":"2024","publication":"Inventiones mathematicae","day":"19","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2210.09064"]},"date_updated":"2025-12-29T12:03:10Z","volume":239,"status":"public","article_processing_charge":"No","extern":"1","OA_type":"green","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2210.09064","open_access":"1"}],"oa_version":"Preprint","date_published":"2024-12-19T00:00:00Z","type":"journal_article","issue":"2","page":"431-468","citation":{"ista":"Berger P, Gourmelon N, Helfter M. 2024. Every diffeomorphism is a total renormalization of a close to identity map. Inventiones mathematicae. 239(2), 431–468.","chicago":"Berger, Pierre, Nicolaz Gourmelon, and Mathieu Helfter. “Every Diffeomorphism Is a Total Renormalization of a Close to Identity Map.” <i>Inventiones Mathematicae</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00222-024-01305-w\">https://doi.org/10.1007/s00222-024-01305-w</a>.","apa":"Berger, P., Gourmelon, N., &#38; Helfter, M. (2024). Every diffeomorphism is a total renormalization of a close to identity map. <i>Inventiones Mathematicae</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00222-024-01305-w\">https://doi.org/10.1007/s00222-024-01305-w</a>","short":"P. Berger, N. Gourmelon, M. Helfter, Inventiones Mathematicae 239 (2024) 431–468.","ama":"Berger P, Gourmelon N, Helfter M. Every diffeomorphism is a total renormalization of a close to identity map. <i>Inventiones mathematicae</i>. 2024;239(2):431-468. doi:<a href=\"https://doi.org/10.1007/s00222-024-01305-w\">10.1007/s00222-024-01305-w</a>","mla":"Berger, Pierre, et al. “Every Diffeomorphism Is a Total Renormalization of a Close to Identity Map.” <i>Inventiones Mathematicae</i>, vol. 239, no. 2, Springer Nature, 2024, pp. 431–68, doi:<a href=\"https://doi.org/10.1007/s00222-024-01305-w\">10.1007/s00222-024-01305-w</a>.","ieee":"P. Berger, N. Gourmelon, and M. Helfter, “Every diffeomorphism is a total renormalization of a close to identity map,” <i>Inventiones mathematicae</i>, vol. 239, no. 2. Springer Nature, pp. 431–468, 2024."},"title":"Every diffeomorphism is a total renormalization of a close to identity map","_id":"20838","language":[{"iso":"eng"}],"abstract":[{"text":"For any 1 ≤ r ≤ ∞, we show that every diffeomorphism of a manifold of the form\r\nR/Z × M is a total renormalization of a Cr-close to identity map. In other words, for\r\nevery diffeomorphism f of R/Z×M, there exists a map g arbitrarily close to identity\r\nsuch that the first return map of g to a domain is conjugate to f and moreover the\r\norbit of this domain is equal to R/Z×M. This enables us to localize near the identity\r\nthe existence of many properties in dynamical systems, such as being Bernoulli for a\r\nsmooth volume form.","lang":"eng"}],"intvolume":"       239","publication_identifier":{"eissn":["1432-1297"],"issn":["0020-9910"]},"quality_controlled":"1","date_created":"2025-12-19T10:15:13Z","doi":"10.1007/s00222-024-01305-w","arxiv":1,"oa":1,"publisher":"Springer Nature","publication_status":"published","article_type":"original","scopus_import":"1"}