[{"day":"07","publisher":"EMS Press","citation":{"short":"M. Helfter, Journal of Fractal Geometry (2025).","mla":"Helfter, Mathieu. “Sets with Arbitrary Hausdorff and Packing Scales in Infinite Dimensional Banach Spaces.” <i>Journal of Fractal Geometry</i>, EMS Press, 2025, doi:<a href=\"https://doi.org/10.4171/jfg/177\">10.4171/jfg/177</a>.","chicago":"Helfter, Mathieu. “Sets with Arbitrary Hausdorff and Packing Scales in Infinite Dimensional Banach Spaces.” <i>Journal of Fractal Geometry</i>. EMS Press, 2025. <a href=\"https://doi.org/10.4171/jfg/177\">https://doi.org/10.4171/jfg/177</a>.","ieee":"M. Helfter, “Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces,” <i>Journal of Fractal Geometry</i>. EMS Press, 2025.","apa":"Helfter, M. (2025). Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces. <i>Journal of Fractal Geometry</i>. EMS Press. <a href=\"https://doi.org/10.4171/jfg/177\">https://doi.org/10.4171/jfg/177</a>","ista":"Helfter M. 2025. Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces. Journal of Fractal Geometry.","ama":"Helfter M. Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces. <i>Journal of Fractal Geometry</i>. 2025. doi:<a href=\"https://doi.org/10.4171/jfg/177\">10.4171/jfg/177</a>"},"year":"2025","_id":"20839","status":"public","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","text":"For every couple of Hausdorff functions ψ and φ verifying some mild assumptions, there exists a compact subset K of the Baire space such that the φ-Hausdorff measure and the ψ-packing measure on K are both finite and positive. Such examples are then embedded in any infinite dimensional Banach space to answer positively a question of Fan on the existence of metric spaces with arbitrary scales."}],"date_updated":"2026-06-18T18:26:33Z","DOAJ_listed":"1","OA_place":"publisher","OA_type":"gold","date_published":"2025-11-07T00:00:00Z","ddc":["500"],"fulldoi":"https://doi.org/10.4171/jfg/177","article_type":"original","month":"11","publication_status":"epub_ahead","department":[{"_id":"VaKa"}],"language":[{"iso":"eng"}],"quality_controlled":"1","article_processing_charge":"Yes","date_created":"2025-12-19T10:15:37Z","publication":"Journal of Fractal Geometry","author":[{"full_name":"Helfter, Mathieu","id":"7d296fbe-e2c6-11ee-84d3-d5c2945f9a57","last_name":"Helfter","first_name":"Mathieu"}],"corr_author":"1","scopus_import":"1","oa":1,"title":"Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces","publication_identifier":{"issn":["2308-1309"],"eissn":["2308-1317"]},"type":"journal_article","doi":"10.4171/jfg/177","main_file_link":[{"open_access":"1","url":"https://doi.org/10.4171/jfg/177"}]},{"article_processing_charge":"No","date_created":"2025-04-06T22:01:32Z","quality_controlled":"1","publication_status":"published","department":[{"_id":"VaKa"}],"volume":310,"language":[{"iso":"eng"}],"month":"05","type":"journal_article","doi":"10.1007/s00209-025-03719-5","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2206.05231"}],"oa":1,"title":"Scales","publication_identifier":{"eissn":["1432-1823"],"issn":["0025-5874"]},"article_number":"15","scopus_import":"1","corr_author":"1","author":[{"full_name":"Helfter, Mathieu","id":"7d296fbe-e2c6-11ee-84d3-d5c2945f9a57","last_name":"Helfter","first_name":"Mathieu"}],"publication":"Mathematische Zeitschrift","intvolume":"       310","external_id":{"arxiv":["2206.05231"],"isi":["001450830300001"]},"oa_version":"Preprint","_id":"19496","status":"public","publisher":"Springer Nature","citation":{"ista":"Helfter M. 2025. Scales. Mathematische Zeitschrift. 310, 15.","ama":"Helfter M. Scales. <i>Mathematische Zeitschrift</i>. 2025;310. doi:<a href=\"https://doi.org/10.1007/s00209-025-03719-5\">10.1007/s00209-025-03719-5</a>","apa":"Helfter, M. (2025). Scales. <i>Mathematische Zeitschrift</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00209-025-03719-5\">https://doi.org/10.1007/s00209-025-03719-5</a>","ieee":"M. Helfter, “Scales,” <i>Mathematische Zeitschrift</i>, vol. 310. Springer Nature, 2025.","chicago":"Helfter, Mathieu. “Scales.” <i>Mathematische Zeitschrift</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00209-025-03719-5\">https://doi.org/10.1007/s00209-025-03719-5</a>.","short":"M. Helfter, Mathematische Zeitschrift 310 (2025).","mla":"Helfter, Mathieu. “Scales.” <i>Mathematische Zeitschrift</i>, vol. 310, 15, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00209-025-03719-5\">10.1007/s00209-025-03719-5</a>."},"year":"2025","isi":1,"arxiv":1,"day":"01","article_type":"original","fulldoi":"https://doi.org/10.1007/s00209-025-03719-5","OA_type":"green","date_published":"2025-05-01T00:00:00Z","OA_place":"repository","date_updated":"2025-09-30T11:31:00Z","abstract":[{"lang":"eng","text":"We introduce the notions of scale for sets and measures on metric space by generalizing the usual notions of dimension. Several versions of scales are introduced such as Hausdorff, packing, box, local and quantization. They are defined for different growth, allowing a refined study of infinite dimensional spaces. We prove general theorems comparing the different versions of scales. They are applied to describe geometries of ergodic decompositions, of the Wiener measure and from functional spaces. The first application solves a problem of Berger on the notions of emergence (2020); the second lies in the geometry of the Wiener measure and extends the work of Dereich–Lifshits (2005); the last refines Kolmogorov–Tikhomirov (1958) study on finitely differentiable functions."}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345"},{"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2210.09064"}],"doi":"10.1007/s00222-024-01305-w","type":"journal_article","publication_identifier":{"eissn":["1432-1297"],"issn":["0020-9910"]},"title":"Every diffeomorphism is a total renormalization of a close to identity map","oa":1,"extern":"1","scopus_import":"1","author":[{"last_name":"Berger","full_name":"Berger, Pierre","first_name":"Pierre"},{"first_name":"Nicolaz","full_name":"Gourmelon, Nicolaz","last_name":"Gourmelon"},{"first_name":"Mathieu","full_name":"Helfter, Mathieu","id":"7d296fbe-e2c6-11ee-84d3-d5c2945f9a57","last_name":"Helfter"}],"publication":"Inventiones mathematicae","date_created":"2025-12-19T10:15:13Z","article_processing_charge":"No","quality_controlled":"1","volume":239,"language":[{"iso":"eng"}],"publication_status":"published","page":"431-468","month":"12","fulldoi":"https://doi.org/10.1007/s00222-024-01305-w","article_type":"original","OA_type":"green","date_published":"2024-12-19T00:00:00Z","OA_place":"repository","date_updated":"2025-12-29T12:03:10Z","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"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"       239","external_id":{"arxiv":["2210.09064"]},"issue":"2","oa_version":"Preprint","status":"public","_id":"20838","year":"2024","citation":{"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.","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>","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.","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>","short":"P. Berger, N. Gourmelon, M. Helfter, Inventiones Mathematicae 239 (2024) 431–468.","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>.","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>."},"publisher":"Springer Nature","day":"19","arxiv":1}]