Benjamín A. Itzá-Ortiz, Mónica Moreno Rocha, Víctor Nopal-Coello
{"title":"Sturmian external angles of primitive components in the Mandelbrot set","authors":"Benjamín A. Itzá-Ortiz, Mónica Moreno Rocha, Víctor Nopal-Coello","doi":"arxiv-2409.07636","DOIUrl":null,"url":null,"abstract":"In this work we introduce the broken line construction, which is a geometric\nand combinatorial algorithm that computes periodic Sturmian angles of a given\nperiod, yielding the locations of their landing parameters in the Mandelbrot\nset. An easy to implement method to compute the conjugated angle of a periodic\nSturmian angle is also provided. Furthermore, if $\\theta$ is a periodic\nSturmian angle computed by the broken line construction, then we show the\nexistence of a one-to-one correspondence between its binary expansion and its\nassociated kneading sequence.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"64 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Dynamical Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.07636","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this work we introduce the broken line construction, which is a geometric
and combinatorial algorithm that computes periodic Sturmian angles of a given
period, yielding the locations of their landing parameters in the Mandelbrot
set. An easy to implement method to compute the conjugated angle of a periodic
Sturmian angle is also provided. Furthermore, if $\theta$ is a periodic
Sturmian angle computed by the broken line construction, then we show the
existence of a one-to-one correspondence between its binary expansion and its
associated kneading sequence.