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Automorphic measures for critical circle maps
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| Author(s): |
Bruno de Almeida Nussenzveig
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) |
| Defense date: | 2023-08-03 |
| Examining board members: |
Edson de Faria;
André Salles de Carvalho;
Pablo Andrés Guarino Quiñones
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| Advisor: | Edson de Faria |
| Abstract | |
Let f be a C^{1 + \\text} circle diffeomorphism with irrational rotation number. As established by Douady and Yoccoz in the eighties, for any given s > 0 there exists a unique automorphic measure of exponent s for f. In the present work we show that the same holds for multicritical circle maps, and we provide two applications of this result. The first one, is to prove that the space of invariant distributions of order 1 of any given multicritical circle map is one-dimensional, spanned by the unique invariant measure. The second one, is an improvement over the Denjoy-Koksma inequality for multicritical circle maps and absolutely continuous observables. (AU) | |
| FAPESP's process: | 21/04599-0 - Multicritical circle maps and invariant distributions |
| Grantee: | Bruno de Almeida Nussenzveig |
| Support Opportunities: | Scholarships in Brazil - Master |