Is the dimension of chaotic attractors invariant under coordinate changes? View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1984-09

AUTHORS

E. Ott, W. D. Withers, J. A. Yorke

ABSTRACT

Several different dimensionlike quantities, which have been suggested as being relevant to the study of chaotic attractors, are examined. In particular, we discuss whether these quantities are invariant under changes of variables that are differentiable except at a finite number of points. It is found that some are and some are not. It is suggested that the word “dimension” be reversed only for those quantities have this invariance property. More... »

PAGES

687-697

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01012932

DOI

http://dx.doi.org/10.1007/bf01012932

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1033195499


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of Maryland, College Park", 
          "id": "https://www.grid.ac/institutes/grid.164295.d", 
          "name": [
            "Department of Electrical Engineering and Department of Physics and Astronomy, University of Maryland, 20742, College Park, Maryland"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Ott", 
        "givenName": "E.", 
        "id": "sg:person.01126615405.17", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01126615405.17"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Maryland, College Park", 
          "id": "https://www.grid.ac/institutes/grid.164295.d", 
          "name": [
            "Department of Mathematics, University of Maryland, 20742, College Park, Maryland"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Withers", 
        "givenName": "W. D.", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Maryland, College Park", 
          "id": "https://www.grid.ac/institutes/grid.164295.d", 
          "name": [
            "Department of Mathematics, University of Maryland, 20742, College Park, Maryland", 
            "Institute for Physical Science and Technology, University of Maryland, 20742, College Park, Maryland"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Yorke", 
        "givenName": "J. A.", 
        "id": "sg:person.01015312776.01", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01015312776.01"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "1984-09", 
    "datePublishedReg": "1984-09-01", 
    "description": "Several different dimensionlike quantities, which have been suggested as being relevant to the study of chaotic attractors, are examined. In particular, we discuss whether these quantities are invariant under changes of variables that are differentiable except at a finite number of points. It is found that some are and some are not. It is suggested that the word \u201cdimension\u201d be reversed only for those quantities have this invariance property.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/bf01012932", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1040979", 
        "issn": [
          "0022-4715", 
          "1572-9613"
        ], 
        "name": "Journal of Statistical Physics", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "5-6", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "36"
      }
    ], 
    "name": "Is the dimension of chaotic attractors invariant under coordinate changes?", 
    "pagination": "687-697", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "9e232d1188c1f9e4c285b8455e119358594e9907fd1aac66b43bd891bf7b1562"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf01012932"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1033195499"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf01012932", 
      "https://app.dimensions.ai/details/publication/pub.1033195499"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T00:12", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8695_00000496.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007/BF01012932"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/bf01012932'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/bf01012932'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf01012932'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf01012932'


 

This table displays all metadata directly associated to this object as RDF triples.

76 TRIPLES      20 PREDICATES      27 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf01012932 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author Na9e6de3c41c947ccac4a8bd3b3e20e19
4 schema:datePublished 1984-09
5 schema:datePublishedReg 1984-09-01
6 schema:description Several different dimensionlike quantities, which have been suggested as being relevant to the study of chaotic attractors, are examined. In particular, we discuss whether these quantities are invariant under changes of variables that are differentiable except at a finite number of points. It is found that some are and some are not. It is suggested that the word “dimension” be reversed only for those quantities have this invariance property.
7 schema:genre research_article
8 schema:inLanguage en
9 schema:isAccessibleForFree false
10 schema:isPartOf N293317e5b5ba48d6b1cfd24901a8bf56
11 Nc95828f172e74646b992bc4cffa55c05
12 sg:journal.1040979
13 schema:name Is the dimension of chaotic attractors invariant under coordinate changes?
14 schema:pagination 687-697
15 schema:productId N2989975a4e164d16b87aa511d26cb6a0
16 N7ed4fc8e42904f75af0358534017149c
17 Nbbc00624a7a74e1587225c7cbc6d2e72
18 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033195499
19 https://doi.org/10.1007/bf01012932
20 schema:sdDatePublished 2019-04-11T00:12
21 schema:sdLicense https://scigraph.springernature.com/explorer/license/
22 schema:sdPublisher Nc7b52322a5e848b984be199f8c7022a5
23 schema:url http://link.springer.com/10.1007/BF01012932
24 sgo:license sg:explorer/license/
25 sgo:sdDataset articles
26 rdf:type schema:ScholarlyArticle
27 N293317e5b5ba48d6b1cfd24901a8bf56 schema:issueNumber 5-6
28 rdf:type schema:PublicationIssue
29 N2989975a4e164d16b87aa511d26cb6a0 schema:name dimensions_id
30 schema:value pub.1033195499
31 rdf:type schema:PropertyValue
32 N4d238c89d6af495fad72c19bb10244ad rdf:first sg:person.01015312776.01
33 rdf:rest rdf:nil
34 N7ed4fc8e42904f75af0358534017149c schema:name readcube_id
35 schema:value 9e232d1188c1f9e4c285b8455e119358594e9907fd1aac66b43bd891bf7b1562
36 rdf:type schema:PropertyValue
37 N8cac71579af04a7fb237f3c69535c1a2 schema:affiliation https://www.grid.ac/institutes/grid.164295.d
38 schema:familyName Withers
39 schema:givenName W. D.
40 rdf:type schema:Person
41 Na9e6de3c41c947ccac4a8bd3b3e20e19 rdf:first sg:person.01126615405.17
42 rdf:rest Nae73b974ff344f6ca38a23eb31ecc581
43 Nae73b974ff344f6ca38a23eb31ecc581 rdf:first N8cac71579af04a7fb237f3c69535c1a2
44 rdf:rest N4d238c89d6af495fad72c19bb10244ad
45 Nbbc00624a7a74e1587225c7cbc6d2e72 schema:name doi
46 schema:value 10.1007/bf01012932
47 rdf:type schema:PropertyValue
48 Nc7b52322a5e848b984be199f8c7022a5 schema:name Springer Nature - SN SciGraph project
49 rdf:type schema:Organization
50 Nc95828f172e74646b992bc4cffa55c05 schema:volumeNumber 36
51 rdf:type schema:PublicationVolume
52 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
53 schema:name Mathematical Sciences
54 rdf:type schema:DefinedTerm
55 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
56 schema:name Pure Mathematics
57 rdf:type schema:DefinedTerm
58 sg:journal.1040979 schema:issn 0022-4715
59 1572-9613
60 schema:name Journal of Statistical Physics
61 rdf:type schema:Periodical
62 sg:person.01015312776.01 schema:affiliation https://www.grid.ac/institutes/grid.164295.d
63 schema:familyName Yorke
64 schema:givenName J. A.
65 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01015312776.01
66 rdf:type schema:Person
67 sg:person.01126615405.17 schema:affiliation https://www.grid.ac/institutes/grid.164295.d
68 schema:familyName Ott
69 schema:givenName E.
70 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01126615405.17
71 rdf:type schema:Person
72 https://www.grid.ac/institutes/grid.164295.d schema:alternateName University of Maryland, College Park
73 schema:name Department of Electrical Engineering and Department of Physics and Astronomy, University of Maryland, 20742, College Park, Maryland
74 Department of Mathematics, University of Maryland, 20742, College Park, Maryland
75 Institute for Physical Science and Technology, University of Maryland, 20742, College Park, Maryland
76 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...