{"title":"三维空间中具有两个不稳定方向的分段双曲图的Sinai-Ruelle-Bowen测度","authors":"Xu Zhang","doi":"10.3934/dcds.2016.36.2873","DOIUrl":null,"url":null,"abstract":"A class of piecewise $C^2$ Lozi-like maps in three-dimensional Euclidean spaces is introduced, and the existence of Sinai-Ruelle-Bowen measures is studied, where the dimension of the instability is equal to two. Further, an example with computer simulations is provided to illustrate the theoretical results.","PeriodicalId":166772,"journal":{"name":"arXiv: Chaotic Dynamics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Sinai-Ruelle-Bowen measures for piecewise hyperbolic maps with two directions of instability in three-dimensional spaces\",\"authors\":\"Xu Zhang\",\"doi\":\"10.3934/dcds.2016.36.2873\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A class of piecewise $C^2$ Lozi-like maps in three-dimensional Euclidean spaces is introduced, and the existence of Sinai-Ruelle-Bowen measures is studied, where the dimension of the instability is equal to two. Further, an example with computer simulations is provided to illustrate the theoretical results.\",\"PeriodicalId\":166772,\"journal\":{\"name\":\"arXiv: Chaotic Dynamics\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-02-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Chaotic Dynamics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/dcds.2016.36.2873\",\"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: Chaotic Dynamics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/dcds.2016.36.2873","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Sinai-Ruelle-Bowen measures for piecewise hyperbolic maps with two directions of instability in three-dimensional spaces
A class of piecewise $C^2$ Lozi-like maps in three-dimensional Euclidean spaces is introduced, and the existence of Sinai-Ruelle-Bowen measures is studied, where the dimension of the instability is equal to two. Further, an example with computer simulations is provided to illustrate the theoretical results.
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