{"@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/1360021390561658752.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.1137/22m1504986"}},{"identifier":{"@type":"DOI","@value":"10.48550/arxiv.2011.12264"}}],"resourceType":"学術雑誌論文(journal article)","dc:title":[{"@value":"Hausdorff Dimension of Cantor Intersections and Robust Heterodimensional Cycles for Heterochaos Horseshoe Maps"}],"description":[{"notation":[{"@value":"As a model to provide a hands-on, elementary understanding of chaotic dynamics in dimension three, we introduce a $C^2$-open set of diffeomorphisms of $\\mathbb R^3$ having two horseshoes with different dimensions of instability. We prove that: the unstable set of one horseshoe and the stable set of the other are of Hausdorff dimension nearly $2$ whose cross sections are Cantor sets; the intersection of the unstable and stable sets contains a fractal set of Hausdorff dimension nearly $1$. As a corollary we detect $C^2$-robust heterodimensional cycles. Our proof employs the theory of normally hyperbolic invariant manifolds and the thicknesses of Cantor sets."}]},{"notation":[{"@value":"25 pages, 9 figures"}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1420564276180821120","@type":"Researcher","personIdentifier":[{"@type":"KAKEN_RESEARCHERS","@value":"00467440"},{"@type":"NRID","@value":"1000000467440"},{"@type":"NRID","@value":"9000240515930"},{"@type":"NRID","@value":"9000415045837"},{"@type":"NRID","@value":"9000410002663"},{"@type":"NRID","@value":"9000002612008"},{"@type":"RESEARCHMAP","@value":"https://researchmap.jp/read00467440"}],"foaf:name":[{"@value":"Hiroki Takahasi"}],"jpcoar:affiliationName":[{"@value":"Keio Institute of Pure and Applied Sciences (KiPAS), Department of Mathematics, Keio University, Yokohama, 223-8522, Japan."}]},{"@id":"https://cir.nii.ac.jp/crid/1380021390561658754","@type":"Researcher","foaf:name":[{"@value":"James A. Yorke"}],"jpcoar:affiliationName":[{"@value":"Institute for Physical Science and Technology and Mathematics and Physics Departments, University of Maryland, College Park, MD 20742, USA."}]},{"@id":"https://cir.nii.ac.jp/crid/1420564276160737024","@type":"Researcher","personIdentifier":[{"@type":"KAKEN_RESEARCHERS","@value":"20433740"},{"@type":"NRID","@value":"1000020433740"},{"@type":"NRID","@value":"9000002362628"},{"@type":"NRID","@value":"9000242656629"},{"@type":"NRID","@value":"9000271150151"},{"@type":"NRID","@value":"9000415146161"},{"@type":"NRID","@value":"9000314080521"},{"@type":"NRID","@value":"9000239574566"},{"@type":"NRID","@value":"9000237872752"},{"@type":"NRID","@value":"9000250187846"},{"@type":"NRID","@value":"9000010674260"},{"@type":"NRID","@value":"9000363905926"},{"@type":"NRID","@value":"9000024871433"},{"@type":"NRID","@value":"9000258441285"},{"@type":"NRID","@value":"9000022096793"},{"@type":"NRID","@value":"9000258442929"},{"@type":"RESEARCHMAP","@value":"https://researchmap.jp/saiki_yoshitaka"}],"foaf:name":[{"@value":"Yoshitaka Saiki"}],"jpcoar:affiliationName":[{"@value":"Graduate School of Business Administration, Hitotsubashi University, Tokyo, 186-8601, Japan."}]}],"publication":{"publicationIdentifier":[{"@type":"EISSN","@value":"15360040"}],"prism:publicationName":[{"@value":"SIAM Journal on Applied Dynamical Systems"}],"dc:publisher":[{"@value":"Society for Industrial & Applied Mathematics (SIAM)"}],"prism:publicationDate":"2023-07-28","prism:volume":"22","prism:number":"3","prism:startingPage":"1852","prism:endingPage":"1876"},"reviewed":"false","createdAt":"2023-07-28","modifiedAt":"2023-09-29","foaf:topic":[{"@id":"https://cir.nii.ac.jp/all?q=FOS:%20Mathematics","dc:title":"FOS: Mathematics"},{"@id":"https://cir.nii.ac.jp/all?q=FOS:%20Physical%20sciences","dc:title":"FOS: Physical sciences"},{"@id":"https://cir.nii.ac.jp/all?q=37C29,%2037D30,%2037G25","dc:title":"37C29, 37D30, 37G25"},{"@id":"https://cir.nii.ac.jp/all?q=Dynamical%20Systems%20(math.DS)","dc:title":"Dynamical Systems (math.DS)"},{"@id":"https://cir.nii.ac.jp/all?q=Mathematics%20-%20Dynamical%20Systems","dc:title":"Mathematics - Dynamical Systems"},{"@id":"https://cir.nii.ac.jp/all?q=Chaotic%20Dynamics%20(nlin.CD)","dc:title":"Chaotic Dynamics (nlin.CD)"},{"@id":"https://cir.nii.ac.jp/all?q=Nonlinear%20Sciences%20-%20Chaotic%20Dynamics","dc:title":"Nonlinear Sciences - Chaotic Dynamics"}],"project":[{"@id":"https://cir.nii.ac.jp/crid/1040295802078563968","@type":"Project","projectIdentifier":[{"@type":"KAKEN","@value":"23H04465"},{"@type":"JGN","@value":"JP23H04465"},{"@type":"URI","@value":"https://kaken.nii.ac.jp/grant/KAKENHI-PUBLICLY-23H04465/"}],"notation":[{"@language":"ja","@value":"回帰を用いたデータ駆動微分方程式モデリング手法の研究"},{"@language":"en","@value":"Data-driven modeling of ordinary differential equations using regression"}]},{"@id":"https://cir.nii.ac.jp/crid/1040566775636386560","@type":"Project","projectIdentifier":[{"@type":"KAKEN","@value":"19K21835"},{"@type":"JGN","@value":"JP19K21835"},{"@type":"URI","@value":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19K21835/"}],"notation":[{"@language":"ja","@value":"漸近双曲性とYoccoz's puzzleを用いたPalis予想解決への挑戦"},{"@language":"en","@value":"A Challenge to the resolution of Palis's conjecture by means of the asymptotic hyperbolicity and Yoccoz's puzzle"}]},{"@id":"https://cir.nii.ac.jp/crid/1040566775637444864","@type":"Project","projectIdentifier":[{"@type":"KAKEN","@value":"19KK0067"},{"@type":"JGN","@value":"JP19KK0067"},{"@type":"URI","@value":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19KK0067/"}],"notation":[{"@language":"ja","@value":"ヘテロカオスにおける間欠性と予測"},{"@language":"en","@value":"Intermittency due to hetero-chaotic property and its inference"}]}],"relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1360011144876492928","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms"}]},{"@id":"https://cir.nii.ac.jp/crid/1360011146231112832","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"ROBUST HETERODIMENSIONAL CYCLES AND $C^1$-GENERIC DYNAMICS"}]},{"@id":"https://cir.nii.ac.jp/crid/1360013168759498112","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Stable intersection of Cantor sets in higher dimension and robust homoclinic tangency of the largest codimension"}]},{"@id":"https://cir.nii.ac.jp/crid/1360021396144205952","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Robust Heteroclinic Tangencies"}]},{"@id":"https://cir.nii.ac.jp/crid/1360021396144964992","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"How big is the intersection of two thick Cantor sets?"}]},{"@id":"https://cir.nii.ac.jp/crid/1360021396146578432","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Stable Intersections of Regular Cantor Sets with Large Hausdorff Dimensions"}]},{"@id":"https://cir.nii.ac.jp/crid/1360294643801189760","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Piecewise linear maps with heterogeneous chaos"}]},{"@id":"https://cir.nii.ac.jp/crid/1360294647834910080","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"C1 density of stable ergodicity"}]},{"@id":"https://cir.nii.ac.jp/crid/1360302868768800256","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Hausdorff dimension for horseshoes in $\\mathbb{R}^3$"}]},{"@id":"https://cir.nii.ac.jp/crid/1360306905176964736","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Exponential Mixing for Heterochaos Baker Maps and the Dyck System"}]},{"@id":"https://cir.nii.ac.jp/crid/1360574093687278080","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Hausdorff dimension for horseshoes"}]},{"@id":"https://cir.nii.ac.jp/crid/1360576121827392896","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"On the continuity of Hausdorff dimension and limit capacity for horseshoes"}]},{"@id":"https://cir.nii.ac.jp/crid/1360576121931608704","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Hyperbolic graphs: Critical regularity and box dimension"}]},{"@id":"https://cir.nii.ac.jp/crid/1360584344420963072","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Limit capacity and hausdorff dimension of dynamically defined cantor sets"}]},{"@id":"https://cir.nii.ac.jp/crid/1360845538929256448","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Fractal Geometry"}]},{"@id":"https://cir.nii.ac.jp/crid/1360855569246296064","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Persistent Nonhyperbolic Transitive Diffeomorphisms"}]},{"@id":"https://cir.nii.ac.jp/crid/1360865820408837120","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"When Cantor sets intersect thickly"}]},{"@id":"https://cir.nii.ac.jp/crid/1361137045110037760","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Bifurcation to infinitely many sinks"}]},{"@id":"https://cir.nii.ac.jp/crid/1361137046142363136","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Abundance of hyperbolicity in the $C^1$ topology"}]},{"@id":"https://cir.nii.ac.jp/crid/1363107369658924928","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Persistence of homoclinic tangencies in higher dimensions"}]},{"@id":"https://cir.nii.ac.jp/crid/1363107370995125504","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Invariant Manifolds"}]},{"@id":"https://cir.nii.ac.jp/crid/1363388843712026368","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Hyperbolic sets exhibiting $C^1$-persistent homoclinic tangency for higher dimensions"}]},{"@id":"https://cir.nii.ac.jp/crid/1363388845745612928","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Nondensity of Axiom A(a) on 𝑆²"}]},{"@id":"https://cir.nii.ac.jp/crid/1363388846335867904","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Persistence and Smoothness of Invariant Manifolds for Flows"}]},{"@id":"https://cir.nii.ac.jp/crid/1363951793181169920","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"There are no C1-stable intersections of regular Cantor sets"}]},{"@id":"https://cir.nii.ac.jp/crid/1363951794174414208","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Diffeomorphisms with infinitely many sinks"}]},{"@id":"https://cir.nii.ac.jp/crid/1363951795709703552","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"High Dimension Diffeomorphisms Displaying Infinitely Many Periodic Attractors"}]},{"@id":"https://cir.nii.ac.jp/crid/1364233271006919680","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"WHAT IS... a Blender?"}]}],"dataSourceIdentifier":[{"@type":"CROSSREF","@value":"10.1137/22m1504986"},{"@type":"KAKEN","@value":"PRODUCT-24279514"},{"@type":"KAKEN","@value":"PRODUCT-25176803"},{"@type":"KAKEN","@value":"PRODUCT-24343989"},{"@type":"KAKEN","@value":"PRODUCT-24845555"},{"@type":"OPENAIRE","@value":"doi_dedup___::62f64e3a4d57f814487398564f6a772b"},{"@type":"CROSSREF","@value":"10.1007/s10884-024-10370-x_references_DOI_FGu4nTJdleZlSxqcKqsWa12NNw6"}]}