Julia Sets of Hyperbolic Rational Maps have Positive Fourier Dimension

Let f : C ^ → C ^ be a hyperbolic rational map of degree d ≥ 2 , and let J ⊂ C be its Julia set. We prove that J always has positive Fourier dimension. The case where J is included in a circle follows from a recent work of Sahlsten and Stevens (Fourier transform and expanding maps on Cantor sets pre...

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Veröffentlicht in:	Communications in mathematical physics 2023-01, Vol.397 (2), p.503-546
1. Verfasser:	Leclerc, Gaétan
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Sprache:	eng
Schlagworte:	Chaotic Dynamics Classical and Quantum Gravitation Complex Systems Dynamical Systems Fourier transforms Mathematical and Computational Physics Mathematical Physics Mathematics Nonlinear Sciences Physics Physics and Astronomy Polynomials Quantum Physics Relativity Theory Theoretical
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description	Let f : C ^ → C ^ be a hyperbolic rational map of degree d ≥ 2 , and let J ⊂ C be its Julia set. We prove that J always has positive Fourier dimension. The case where J is included in a circle follows from a recent work of Sahlsten and Stevens (Fourier transform and expanding maps on Cantor sets preprint. arXiv:2009.01703 , 2020). In the case where J is not included in a circle, we prove that a large family of probability measures supported on J exhibit polynomial Fourier decay: our result applies in particular to the measure of maximal entropy and to the conformal measure.
doi_str_mv	10.1007/s00220-022-04496-6
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In the case where J is not included in a circle, we prove that a large family of probability measures supported on J exhibit polynomial Fourier decay: our result applies in particular to the measure of maximal entropy and to the conformal measure.</description><subject>Chaotic Dynamics</subject><subject>Classical and Quantum Gravitation</subject><subject>Complex Systems</subject><subject>Dynamical Systems</subject><subject>Fourier transforms</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Physics</subject><subject>Mathematics</subject><subject>Nonlinear Sciences</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Polynomials</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Theoretical</subject><issn>0010-3616</issn><issn>1432-0916</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kM1OAyEUhYnRxFp9AVckrlyM3guUGZZNtVZTo_FnTSjDWJppp8K0Sd9e6hjduTlwyXdOLoeQc4QrBMivIwBjkCXJQAglM3lAeih4GhXKQ9IDQMi4RHlMTmJcAIBiUvbI-GFTe0NfXRtpU9HJbu3CrKm9pS-m9c3K1PTRrCOdm62jz030rU-XcbMJ3gV645duFRN2So4qU0d39nP2yfv49m00yaZPd_ej4TSzHESb8YFA4wQWJi9tZZEBWls4sMpiyVVVKJxJVvKqmomi5AjciMKhEMALMAPG--Syy52bWq-DX5qw043xejKc6v0b8Lxgg7zYYmIvOnYdms-Ni61epLXTj6JmuVRMKMR9IusoG5oYg6t-YxH0vlvddauT6O9utUwm3pliglcfLvxF_-P6AiygefA</recordid><startdate>20230101</startdate><enddate>20230101</enddate><creator>Leclerc, Gaétan</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0001-9424-6420</orcidid></search><sort><creationdate>20230101</creationdate><title>Julia Sets of Hyperbolic Rational Maps have Positive Fourier Dimension</title><author>Leclerc, Gaétan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c304t-3541ae418a7dcfc1201cc8e0c9c1d39f891b62d3ffb48d3103a48e1440380a523</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Chaotic Dynamics</topic><topic>Classical and Quantum Gravitation</topic><topic>Complex Systems</topic><topic>Dynamical Systems</topic><topic>Fourier transforms</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Physics</topic><topic>Mathematics</topic><topic>Nonlinear Sciences</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Polynomials</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Leclerc, Gaétan</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Communications in mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Leclerc, Gaétan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Julia Sets of Hyperbolic Rational Maps have Positive Fourier Dimension</atitle><jtitle>Communications in mathematical physics</jtitle><stitle>Commun. 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subjects	Chaotic Dynamics Classical and Quantum Gravitation Complex Systems Dynamical Systems Fourier transforms Mathematical and Computational Physics Mathematical Physics Mathematics Nonlinear Sciences Physics Physics and Astronomy Polynomials Quantum Physics Relativity Theory Theoretical
title	Julia Sets of Hyperbolic Rational Maps have Positive Fourier Dimension
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