{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1040862776831248000.json","@type":"Project","projectIdentifier":[{"@type":"KAKEN","@value":"23K20806"},{"@type":"JGN","@value":"JP23K20806"},{"@type":"URI","@value":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23K20806/"}],"jpcoar:awardTitle":[{"@language":"ja","@value":"アノソフ流の指数混合性と量子カオスの諸問題"},{"@language":"en","@value":"Exponential mixing property of Anosov flows and some related topics in quantum chaos"}],"field":[{"keyword":[{"language":"ja","textList":["小区分12020:数理解析学関連"]},{"language":"en","textList":["Basic Section 12020:Mathematical analysis-related"]}]}],"dc:language":"ja","description":[{"type":"outline_of_research_initial","notation":[{"@language":"ja","@value":"自然界の諸現象を記述するために、科学では時間経過に伴う変化を「力学系」という数学的対象で表現します。この中には、系自体は単純でも、その振る舞いが複雑で予測不可能になることがあり、「カオス」と呼ばれます。カオスを記述し、解析する方法は、力学系理論において最も重要な課題の１つです。本研究は、特に典型的なカオスの一形態であるアノソフ流に対して理論的で精密な解析を行います。興味深いことに、この研究の中で量子力学との類似性が発見され、多くの研究者の注目を集めています。本研究は、この分野において主導的な役割を果たすことを目指しています。"}]}],"researcher":[{"@id":"https://cir.nii.ac.jp/crid/1420282801194745600","@type":"Researcher","personIdentifier":[{"@type":"KAKEN_RESEARCHERS","@value":"20251598"},{"@type":"NRID","@value":"1000020251598"},{"@type":"NRID","@value":"9000002359953"},{"@type":"NRID","@value":"9000380479152"},{"@type":"NRID","@value":"9000254307214"},{"@type":"NRID","@value":"9000017049550"},{"@type":"NRID","@value":"9000254724379"},{"@type":"NRID","@value":"9000396107569"},{"@type":"NRID","@value":"9000261664869"},{"@type":"NRID","@value":"9000016610450"},{"@type":"NRID","@value":"9000240065148"},{"@type":"NRID","@value":"9000023769218"},{"@type":"NRID","@value":"9000254727215"},{"@type":"NRID","@value":"9000018991455"},{"@type":"NRID","@value":"9000389445047"},{"@type":"NRID","@value":"9000273394682"},{"@type":"NRID","@value":"9000356550817"},{"@type":"NRID","@value":"9000023750703"},{"@type":"RESEARCHMAP","@value":"https://researchmap.jp/masatotsujii"}],"foaf:name":[{"@language":"ja","@value":"辻井 正人"}],"jpcoar:affiliationName":[{"@language":"ja","@value":"九州大学"}],"role":"principal_investigator"}],"since":"2024-04-01","until":"2026-03-31","institution":[{"institutionIdentifier":[{"@type":"NII","@value":"0017102"}],"notation":[{"@language":"ja","@value":"九州大学"},{"@language":"en","@value":"Kyushu University"}]}],"fundingProgram":[{"jpcoar:funderName":[{"@language":"ja","@value":"科学研究費助成事業"},{"@language":"en","@value":"Grants-in-Aid for Scientific Research"}]}],"url":[{"@id":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23K20806/","notation":[{"@value":"KAKEN"}]}],"createdAt":"2021-04-28","modifiedAt":"2025-12-26","foaf:topic":[{"@id":"https://cir.nii.ac.jp/all?q=%E5%8A%9B%E5%AD%A6%E7%B3%BB","dc:title":"力学系"},{"@id":"https://cir.nii.ac.jp/all?q=%E3%82%AB%E3%82%AA%E3%82%B9","dc:title":"カオス"},{"@id":"https://cir.nii.ac.jp/all?q=%E9%83%A8%E5%88%86%E5%8F%8C%E6%9B%B2%E5%8A%9B%E5%AD%A6%E7%B3%BB","dc:title":"部分双曲力学系"},{"@id":"https://cir.nii.ac.jp/all?q=%E5%AE%89%E5%AE%9A%E8%91%89%E5%B1%A4","dc:title":"安定葉層"},{"@id":"https://cir.nii.ac.jp/all?q=%E3%82%A2%E3%83%8E%E3%82%BD%E3%83%95%E6%B5%81","dc:title":"アノソフ流"},{"@id":"https://cir.nii.ac.jp/all?q=%E6%B8%AC%E5%9C%B0%E6%B5%81","dc:title":"測地流"},{"@id":"https://cir.nii.ac.jp/all?q=%E3%82%A8%E3%83%AB%E3%82%B4%E3%83%BC%E3%83%89%E7%90%86%E8%AB%96","dc:title":"エルゴード理論"},{"@id":"https://cir.nii.ac.jp/all?q=%E5%BE%AE%E5%88%86%E5%8F%AF%E8%83%BD%E5%8A%9B%E5%AD%A6%E7%B3%BB","dc:title":"微分可能力学系"},{"@id":"https://cir.nii.ac.jp/all?q=Anosov%20%E6%B5%81","dc:title":"Anosov 流"},{"@id":"https://cir.nii.ac.jp/all?q=%E6%B3%A2%E6%9D%9F%E5%A4%89%E6%8F%9B","dc:title":"波束変換"},{"@id":"https://cir.nii.ac.jp/all?q=%E4%B8%8D%E5%A4%89%E8%91%89%E5%B1%A4","dc:title":"不変葉層"},{"@id":"https://cir.nii.ac.jp/all?q=%E8%BB%A2%E9%80%81%E4%BD%9C%E7%94%A8%E7%B4%A0","dc:title":"転送作用素"},{"@id":"https://cir.nii.ac.jp/all?q=%E3%83%95%E3%83%BC%E3%83%AA%E3%82%A8%E5%A4%89%E6%8F%9B","dc:title":"フーリエ変換"},{"@id":"https://cir.nii.ac.jp/all?q=%E5%8F%8C%E6%9B%B2%E5%8A%9B%E5%AD%A6%E7%B3%BB","dc:title":"双曲力学系"},{"@id":"https://cir.nii.ac.jp/all?q=%E6%BA%96%E5%8F%A4%E5%85%B8%E8%A7%A3%E6%9E%90","dc:title":"準古典解析"},{"@id":"https://cir.nii.ac.jp/all?q=%E6%8C%87%E6%95%B0%E6%B7%B7%E5%90%88%E6%80%A7","dc:title":"指数混合性"}],"product":[{"@id":"https://cir.nii.ac.jp/crid/1360588379391761536","@type":"Article","resourceType":"学術雑誌論文(journal article)","productIdentifier":[{"@type":"DOI","@value":"10.1017/etds.2023.11"},{"@type":"URI","@value":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0143385723000111"}],"notation":[{"@value":"On bifurcation of statistical properties of partially hyperbolic endomorphisms"}]},{"@id":"https://cir.nii.ac.jp/crid/1390297814401652736","@type":"Article","resourceType":"学術雑誌論文(journal article)","productIdentifier":[{"@type":"DOI","@value":"10.2206/kyushujm.77.291"},{"@type":"URI","@value":"https://www.jstage.jst.go.jp/article/kyushujm/77/2/77_291/_pdf"},{"@type":"DOI","@value":"10.48550/arxiv.2203.16103"}],"notation":[{"@language":"en","@value":"VIRTUALLY EXPANDING DYNAMICS"}]},{"@id":"https://cir.nii.ac.jp/crid/1360588379400102528","@type":"Article","resourceType":"学術雑誌論文(journal article)","productIdentifier":[{"@type":"DOI","@value":"10.5802/ahl.167"},{"@type":"URI","@value":"https://ahl.centre-mersenne.org/item/10.5802/ahl.167.pdf"}],"notation":[{"@value":"Fractal Weyl law for the Ruelle spectrum of Anosov flows"}]},{"@id":"https://cir.nii.ac.jp/crid/1360306905638317184","@type":"Article","resourceType":"学術雑誌論文(journal article)","productIdentifier":[{"@type":"DOI","@value":"10.1090/cams/40"},{"@type":"URI","@value":"https://www.ams.org/cams/2024-04-15/S2692-3688-2024-00040-8/S2692-3688-2024-00040-8.pdf"}],"notation":[{"@value":"Micro-local analysis of contact Anosov flows and band structure of the Ruelle spectrum"}]},{"@id":"https://cir.nii.ac.jp/crid/1360588380165010560","@type":"Article","resourceType":"学術雑誌論文(journal article)","productIdentifier":[{"@type":"DOI","@value":"10.4007/annals.2023.197.1.2"},{"@type":"DOI","@value":"10.48550/arxiv.2006.04293"}],"notation":[{"@value":"Smooth mixing Anosov flows in dimension three are exponentially mixing"}]},{"@id":"https://cir.nii.ac.jp/crid/1360298755637960960","@type":"Article","resourceType":"学術雑誌論文(journal article)","productIdentifier":[{"@type":"DOI","@value":"10.1016/j.jmaa.2022.126163"},{"@type":"URI","@value":"https://api.elsevier.com/content/article/PII:S0022247X22001779?httpAccept=text/xml"},{"@type":"URI","@value":"https://api.elsevier.com/content/article/PII:S0022247X22001779?httpAccept=text/plain"}],"notation":[{"@value":"Invariant densities for random continued fractions"}]}],"dataSourceIdentifier":[{"@type":"KAKEN","@value":"23K20806"}],"grant":{"grantIdentifier":[{"@type":"NII","@value":"69"}],"jpcoar:fundingStream":[{"@language":"ja","@value":"基盤研究(B)"},{"@language":"en","@value":"Grant-in-Aid for Scientific Research (B)"}]},"allocationClassification":[{"notation":[{"@language":"ja","@value":"基金"},{"@language":"en","@value":"Multi-year Fund"}]},{"notation":[{"@language":"ja","@value":"補助金"},{"@language":"en","@value":"Single-year Grants"}]}],"projectStatus":"granted","allocationAmount":{"totalCost":{"amount":"17160000","currency":"JPY"},"breakdownCost":[{"notation":[{"@language":"ja","@value":"直接経費"},{"@language":"en","@value":"Direct Cost"}],"amount":"13200000","currency":"JPY"},{"notation":[{"@language":"ja","@value":"間接経費"},{"@language":"en","@value":"Indirect Cost"}],"amount":"3960000","currency":"JPY"}]}}