{"title":"刘维尔频率的综合状态密度的荷尔德连续性","authors":"Rui Han, Wilhelm Schlag","doi":"arxiv-2408.15962","DOIUrl":null,"url":null,"abstract":"We prove H\\\"older continuity of the Lyapunov exponent $L(\\omega,E)$ and the\nintegrated density of states at energies that satisfy\n$L(\\omega,E)>4\\kappa(\\omega,E)\\cdot \\beta(\\omega)\\geq 0$ for general analytic\npotentials, with $\\kappa(\\omega,E)$ being Avila's acceleration.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"13 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hölder continuity of the integrated density of states for Liouville frequencies\",\"authors\":\"Rui Han, Wilhelm Schlag\",\"doi\":\"arxiv-2408.15962\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove H\\\\\\\"older continuity of the Lyapunov exponent $L(\\\\omega,E)$ and the\\nintegrated density of states at energies that satisfy\\n$L(\\\\omega,E)>4\\\\kappa(\\\\omega,E)\\\\cdot \\\\beta(\\\\omega)\\\\geq 0$ for general analytic\\npotentials, with $\\\\kappa(\\\\omega,E)$ being Avila's acceleration.\",\"PeriodicalId\":501373,\"journal\":{\"name\":\"arXiv - MATH - Spectral Theory\",\"volume\":\"13 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Spectral Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.15962\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Spectral Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.15962","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Hölder continuity of the integrated density of states for Liouville frequencies
We prove H\"older continuity of the Lyapunov exponent $L(\omega,E)$ and the
integrated density of states at energies that satisfy
$L(\omega,E)>4\kappa(\omega,E)\cdot \beta(\omega)\geq 0$ for general analytic
potentials, with $\kappa(\omega,E)$ being Avila's acceleration.
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