On the classes of Lipschitz and smooth conjugacies of unimodal maps
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| Title: | On the classes of Lipschitz and smooth conjugacies of unimodal maps |
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| Authors: | Waldemar Pałuba |
| Source: | Fundamenta Mathematicae. 183:215-227 |
| Publisher Information: | Institute of Mathematics, Polish Academy of Sciences, 2004. |
| Publication Year: | 2004 |
| Subject Terms: | Dynamical systems involving maps of the interval, Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems, \(C^1\)-unimodal maps, 0103 physical sciences, conjugacy, Lipschitz condition, 0101 mathematics, \(C^1\)-smoothness, 01 natural sciences |
| Description: | Summary: Under very mild assumptions, any Lipschitz continuous conjugacy between the closures of the postcritical sets of two \(C^1\)-unimodal maps has a derivative at the critical point, and also on a dense set of its preimages. In a more restrictive situation of infinitely renormalizable maps of bounded combinatorial type, the Lipschitz condition automatically implies the \(C^1\)-smoothness of the conjugacy. Here, the critical degree can be any real number \(\alpha> 1\). |
| Document Type: | Article |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 1730-6329 0016-2736 |
| DOI: | 10.4064/fm183-3-2 |
| Access URL: | https://www.impan.pl/shop/publication/transaction/download/product/88999?download.pdf https://zbmath.org/2159593 https://doi.org/10.4064/fm183-3-2 http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-fm183-3-2 https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/fundamenta-mathematicae/all/183/3/88999/on-the-classes-of-lipschitz-and-smooth-conjugacies-of-unimodal-maps https://www.impan.pl/shop/publication/transaction/download/product/88999?download.pdf |
| Accession Number: | edsair.doi.dedup.....3ca02db58bef6f8066e78a3d20067fe0 |
| Database: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstract: | Summary: Under very mild assumptions, any Lipschitz continuous conjugacy between the closures of the postcritical sets of two \(C^1\)-unimodal maps has a derivative at the critical point, and also on a dense set of its preimages. In a more restrictive situation of infinitely renormalizable maps of bounded combinatorial type, the Lipschitz condition automatically implies the \(C^1\)-smoothness of the conjugacy. Here, the critical degree can be any real number \(\alpha> 1\). |
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| ISSN: | 17306329 00162736 |
| DOI: | 10.4064/fm183-3-2 |