{"title":"图定向平面非共形度量的 L q谱","authors":"Hua Qiu, Qi Wang and Shufang Wang","doi":"10.1088/1361-6544/ad6055","DOIUrl":null,"url":null,"abstract":"We estimate the upper and lower Lq-spectra of measures generated by a class of graph-directed planar non-conformal iterated function systems. These systems are composed of contractions with lower triangular pointwise Jacobian. The estimation provides a criterion for the existence of the Lq-spectra in certain case. As an application, we derive the box-counting dimension of planar self-affine sets generated by lower triangular matrices, whose geometric construction satisfies a finite overlapping type condition.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"47 1","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"L q -spectra of graph-directed planar non-conformal measures\",\"authors\":\"Hua Qiu, Qi Wang and Shufang Wang\",\"doi\":\"10.1088/1361-6544/ad6055\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We estimate the upper and lower Lq-spectra of measures generated by a class of graph-directed planar non-conformal iterated function systems. These systems are composed of contractions with lower triangular pointwise Jacobian. The estimation provides a criterion for the existence of the Lq-spectra in certain case. As an application, we derive the box-counting dimension of planar self-affine sets generated by lower triangular matrices, whose geometric construction satisfies a finite overlapping type condition.\",\"PeriodicalId\":54715,\"journal\":{\"name\":\"Nonlinearity\",\"volume\":\"47 1\",\"pages\":\"\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2024-07-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinearity\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1088/1361-6544/ad6055\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinearity","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1088/1361-6544/ad6055","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
L q -spectra of graph-directed planar non-conformal measures
We estimate the upper and lower Lq-spectra of measures generated by a class of graph-directed planar non-conformal iterated function systems. These systems are composed of contractions with lower triangular pointwise Jacobian. The estimation provides a criterion for the existence of the Lq-spectra in certain case. As an application, we derive the box-counting dimension of planar self-affine sets generated by lower triangular matrices, whose geometric construction satisfies a finite overlapping type condition.
期刊介绍：
Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest.
Subject coverage:
The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal.
Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena.
Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.
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