Absolutely continuous invariant measures for one-parameter families of one-dimensional maps View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1981-09

AUTHORS

M. V. Jakobson

ABSTRACT

Given a one-parameter familyfλ(x) of maps of the interval [0, 1], we consider the set of parameter values λ for whichfλ has an invariant measure absolutely continuous with respect to Lebesgue measure. We show that this set has positive measure, for two classes of maps: i)fλ(x)=λf(x) where 0<λ≦4 andf(x) is a functionC3-near the quadratic mapx(1−x), and ii)fλ(x)=λf(x) (mod 1) wheref isC3,f(0)=f(1)=0 andf has a unique nondegenerate critical point in [0, 1]. More... »

PAGES

39-88

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01941800

DOI

http://dx.doi.org/10.1007/bf01941800

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1036786184


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/2008/1701", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Psychology", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/17", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Psychology and Cognitive Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "name": [
            "Central Scientific-Research Economic Institute, Smolenskii Boulevard, G-117, Moscow, USSR"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Jakobson", 
        "givenName": "M. V.", 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bf02591353", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003673997", 
          "https://doi.org/10.1007/bf02591353"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01198121", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006385924", 
          "https://doi.org/10.1007/bf01198121"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01198121", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006385924", 
          "https://doi.org/10.1007/bf01198121"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01613148", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1013453626", 
          "https://doi.org/10.1007/bf01613148"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01613148", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1013453626", 
          "https://doi.org/10.1007/bf01613148"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0002-9947-1978-0466493-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1014225071"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02698686", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1016204036", 
          "https://doi.org/10.1007/bf02698686"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01982351", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028474229", 
          "https://doi.org/10.1007/bf01982351"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01982351", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028474229", 
          "https://doi.org/10.1007/bf01982351"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01941319", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1051661871", 
          "https://doi.org/10.1007/bf01941319"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01941319", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1051661871", 
          "https://doi.org/10.1007/bf01941319"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.3836/tjm/1270216320", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1071449069"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1981-09", 
    "datePublishedReg": "1981-09-01", 
    "description": "Given a one-parameter familyf\u03bb(x) of maps of the interval [0, 1], we consider the set of parameter values \u03bb for whichf\u03bb has an invariant measure absolutely continuous with respect to Lebesgue measure. We show that this set has positive measure, for two classes of maps: i)f\u03bb(x)=\u03bbf(x) where 0<\u03bb\u22664 andf(x) is a functionC3-near the quadratic mapx(1\u2212x), and ii)f\u03bb(x)=\u03bbf(x) (mod 1) wheref isC3,f(0)=f(1)=0 andf has a unique nondegenerate critical point in [0, 1].", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/bf01941800", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136216", 
        "issn": [
          "0010-3616", 
          "1432-0916"
        ], 
        "name": "Communications in Mathematical Physics", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "81"
      }
    ], 
    "name": "Absolutely continuous invariant measures for one-parameter families of one-dimensional maps", 
    "pagination": "39-88", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "af3c63c35cdf4038692c4d37f42e2ca2eafe0afb648c92c4ddf2be8308af36c8"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf01941800"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1036786184"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf01941800", 
      "https://app.dimensions.ai/details/publication/pub.1036786184"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T11:09", 
    "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/v90/0000000353_0000000353/records_45340_00000000.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007/BF01941800"
  }
]
 

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/bf01941800'

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/bf01941800'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf01941800'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf01941800'


 

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

89 TRIPLES      21 PREDICATES      35 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf01941800 schema:about anzsrc-for:17
2 anzsrc-for:1701
3 schema:author N864902d715364ce6a73ed802181f6b4a
4 schema:citation sg:pub.10.1007/bf01198121
5 sg:pub.10.1007/bf01613148
6 sg:pub.10.1007/bf01941319
7 sg:pub.10.1007/bf01982351
8 sg:pub.10.1007/bf02591353
9 sg:pub.10.1007/bf02698686
10 https://doi.org/10.1090/s0002-9947-1978-0466493-1
11 https://doi.org/10.3836/tjm/1270216320
12 schema:datePublished 1981-09
13 schema:datePublishedReg 1981-09-01
14 schema:description Given a one-parameter familyfλ(x) of maps of the interval [0, 1], we consider the set of parameter values λ for whichfλ has an invariant measure absolutely continuous with respect to Lebesgue measure. We show that this set has positive measure, for two classes of maps: i)fλ(x)=λf(x) where 0<λ≦4 andf(x) is a functionC3-near the quadratic mapx(1−x), and ii)fλ(x)=λf(x) (mod 1) wheref isC3,f(0)=f(1)=0 andf has a unique nondegenerate critical point in [0, 1].
15 schema:genre research_article
16 schema:inLanguage en
17 schema:isAccessibleForFree false
18 schema:isPartOf N826d56445a8e475cb6b101e452847830
19 Ndf2e7f705ba942df8826f77e94876835
20 sg:journal.1136216
21 schema:name Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
22 schema:pagination 39-88
23 schema:productId N6902db0e6a854539a2144d2e1afb8661
24 N79045f69ee1a4952b22c2962c7d61d04
25 Nef010f76151d42a3bbf39de036a1750d
26 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036786184
27 https://doi.org/10.1007/bf01941800
28 schema:sdDatePublished 2019-04-11T11:09
29 schema:sdLicense https://scigraph.springernature.com/explorer/license/
30 schema:sdPublisher N8ab64bf55d004dfcbe5879c2a987b63c
31 schema:url http://link.springer.com/10.1007/BF01941800
32 sgo:license sg:explorer/license/
33 sgo:sdDataset articles
34 rdf:type schema:ScholarlyArticle
35 N0d3a0655d099469d84f59490210791a1 schema:affiliation N79feb37d66714469af3772a0c1d87162
36 schema:familyName Jakobson
37 schema:givenName M. V.
38 rdf:type schema:Person
39 N6902db0e6a854539a2144d2e1afb8661 schema:name dimensions_id
40 schema:value pub.1036786184
41 rdf:type schema:PropertyValue
42 N79045f69ee1a4952b22c2962c7d61d04 schema:name doi
43 schema:value 10.1007/bf01941800
44 rdf:type schema:PropertyValue
45 N79feb37d66714469af3772a0c1d87162 schema:name Central Scientific-Research Economic Institute, Smolenskii Boulevard, G-117, Moscow, USSR
46 rdf:type schema:Organization
47 N826d56445a8e475cb6b101e452847830 schema:issueNumber 1
48 rdf:type schema:PublicationIssue
49 N864902d715364ce6a73ed802181f6b4a rdf:first N0d3a0655d099469d84f59490210791a1
50 rdf:rest rdf:nil
51 N8ab64bf55d004dfcbe5879c2a987b63c schema:name Springer Nature - SN SciGraph project
52 rdf:type schema:Organization
53 Ndf2e7f705ba942df8826f77e94876835 schema:volumeNumber 81
54 rdf:type schema:PublicationVolume
55 Nef010f76151d42a3bbf39de036a1750d schema:name readcube_id
56 schema:value af3c63c35cdf4038692c4d37f42e2ca2eafe0afb648c92c4ddf2be8308af36c8
57 rdf:type schema:PropertyValue
58 anzsrc-for:17 schema:inDefinedTermSet anzsrc-for:
59 schema:name Psychology and Cognitive Sciences
60 rdf:type schema:DefinedTerm
61 anzsrc-for:1701 schema:inDefinedTermSet anzsrc-for:
62 schema:name Psychology
63 rdf:type schema:DefinedTerm
64 sg:journal.1136216 schema:issn 0010-3616
65 1432-0916
66 schema:name Communications in Mathematical Physics
67 rdf:type schema:Periodical
68 sg:pub.10.1007/bf01198121 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006385924
69 https://doi.org/10.1007/bf01198121
70 rdf:type schema:CreativeWork
71 sg:pub.10.1007/bf01613148 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013453626
72 https://doi.org/10.1007/bf01613148
73 rdf:type schema:CreativeWork
74 sg:pub.10.1007/bf01941319 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051661871
75 https://doi.org/10.1007/bf01941319
76 rdf:type schema:CreativeWork
77 sg:pub.10.1007/bf01982351 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028474229
78 https://doi.org/10.1007/bf01982351
79 rdf:type schema:CreativeWork
80 sg:pub.10.1007/bf02591353 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003673997
81 https://doi.org/10.1007/bf02591353
82 rdf:type schema:CreativeWork
83 sg:pub.10.1007/bf02698686 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016204036
84 https://doi.org/10.1007/bf02698686
85 rdf:type schema:CreativeWork
86 https://doi.org/10.1090/s0002-9947-1978-0466493-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014225071
87 rdf:type schema:CreativeWork
88 https://doi.org/10.3836/tjm/1270216320 schema:sameAs https://app.dimensions.ai/details/publication/pub.1071449069
89 rdf:type schema:CreativeWork
 




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


...