Ergodic theory:
The study of dynamical systems forms a vast and rapidly developing field even when one considers only activity whose methods derive mainly from measure theory and functional analysis. Karl Petersen has written a book which presents the fundamentals of the ergodic theory of point transformations and...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1989
|
| Schriftenreihe: | Cambridge studies in advanced mathematics
2 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | The study of dynamical systems forms a vast and rapidly developing field even when one considers only activity whose methods derive mainly from measure theory and functional analysis. Karl Petersen has written a book which presents the fundamentals of the ergodic theory of point transformations and then several advanced topics which are currently undergoing intense research. By selecting one or more of these topics to focus on, the reader can quickly approach the specialized literature and indeed the frontier of the area of interest. Each of the four basic aspects of ergodic theory - examples, convergence theorems, recurrence properties, and entropy - receives first a basic and then a more advanced, particularized treatment. At the introductory level, the book provides clear and complete discussions of the standard examples, the mean and pointwise ergodic theorems, recurrence, ergodicity, weak mixing, strong mixing, and the fundamentals of entropy. Among the advanced topics are a thorough treatment of maximal functions and their usefulness in ergodic theory, analysis, and probability, an introduction to almost-periodic functions and topological dynamics, a proof of the Jewett-Krieger Theorem, an introduction to multiple recurrence and the Szemeredi-Furstenberg Theorem, and the Keane-Smorodinsky proof of Ornstein's Isomorphism Theorem for Bernoulli shifts. The author's easily-readable style combined with the profusion of exercises and references, summaries, historical remarks, and heuristic discussions make this book useful either as a text for graduate students or self-study, or as a reference work for the initiated |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 Online-Ressource (xi, 329 Seiten) |
| ISBN: | 9780511608728 |
| DOI: | 10.1017/CBO9780511608728 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043940673 | ||
| 003 | DE-604 | ||
| 005 | 20190222 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 161206s1989 |||| o||u| ||||||eng d | ||
| 020 | |a 9780511608728 |c Online |9 978-0-511-60872-8 | ||
| 024 | 7 | |a 10.1017/CBO9780511608728 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9780511608728 | ||
| 035 | |a (OCoLC)992843327 | ||
| 035 | |a (DE-599)BVBBV043940673 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 |a DE-355 | ||
| 082 | 0 | |a 515/.42 |2 20 | |
| 084 | |a SK 810 |0 (DE-625)143257: |2 rvk | ||
| 100 | 1 | |a Petersen, Karl Endel |d 1943- |e Verfasser |0 (DE-588)14248394X |4 aut | |
| 245 | 1 | 0 | |a Ergodic theory |c Karl Petersen |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 1989 | |
| 300 | |a 1 Online-Ressource (xi, 329 Seiten) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Cambridge studies in advanced mathematics |v 2 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 520 | |a The study of dynamical systems forms a vast and rapidly developing field even when one considers only activity whose methods derive mainly from measure theory and functional analysis. Karl Petersen has written a book which presents the fundamentals of the ergodic theory of point transformations and then several advanced topics which are currently undergoing intense research. By selecting one or more of these topics to focus on, the reader can quickly approach the specialized literature and indeed the frontier of the area of interest. Each of the four basic aspects of ergodic theory - examples, convergence theorems, recurrence properties, and entropy - receives first a basic and then a more advanced, particularized treatment. At the introductory level, the book provides clear and complete discussions of the standard examples, the mean and pointwise ergodic theorems, recurrence, ergodicity, weak mixing, strong mixing, and the fundamentals of entropy. Among the advanced topics are a thorough treatment of maximal functions and their usefulness in ergodic theory, analysis, and probability, an introduction to almost-periodic functions and topological dynamics, a proof of the Jewett-Krieger Theorem, an introduction to multiple recurrence and the Szemeredi-Furstenberg Theorem, and the Keane-Smorodinsky proof of Ornstein's Isomorphism Theorem for Bernoulli shifts. The author's easily-readable style combined with the profusion of exercises and references, summaries, historical remarks, and heuristic discussions make this book useful either as a text for graduate students or self-study, or as a reference work for the initiated | ||
| 650 | 4 | |a Ergodic theory | |
| 650 | 0 | 7 | |a Ergodentheorie |0 (DE-588)4015246-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Ergodentheorie |0 (DE-588)4015246-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 978-0-521-23632-4 |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 978-0-521-38997-6 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/CBO9780511608728 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029349643 | ||
| 966 | e | |u https://doi.org/10.1017/CBO9780511608728 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511608728 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511608728 |l UBR01 |p ZDB-20-CBO |q UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804176881483776000 |
|---|---|
| any_adam_object | |
| author | Petersen, Karl Endel 1943- |
| author_GND | (DE-588)14248394X |
| author_facet | Petersen, Karl Endel 1943- |
| author_role | aut |
| author_sort | Petersen, Karl Endel 1943- |
| author_variant | k e p ke kep |
| building | Verbundindex |
| bvnumber | BV043940673 |
| classification_rvk | SK 810 |
| collection | ZDB-20-CBO |
| ctrlnum | (ZDB-20-CBO)CR9780511608728 (OCoLC)992843327 (DE-599)BVBBV043940673 |
| dewey-full | 515/.42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.42 |
| dewey-search | 515/.42 |
| dewey-sort | 3515 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511608728 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03549nmm a2200469zcb4500</leader><controlfield tag="001">BV043940673</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20190222 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">161206s1989 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511608728</subfield><subfield code="c">Online</subfield><subfield code="9">978-0-511-60872-8</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/CBO9780511608728</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9780511608728</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)992843327</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043940673</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-92</subfield><subfield code="a">DE-355</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.42</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 810</subfield><subfield code="0">(DE-625)143257:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Petersen, Karl Endel</subfield><subfield code="d">1943-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)14248394X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Ergodic theory</subfield><subfield code="c">Karl Petersen</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">1989</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (xi, 329 Seiten)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Cambridge studies in advanced mathematics</subfield><subfield code="v">2</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from publisher's bibliographic system (viewed on 05 Oct 2015)</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The study of dynamical systems forms a vast and rapidly developing field even when one considers only activity whose methods derive mainly from measure theory and functional analysis. Karl Petersen has written a book which presents the fundamentals of the ergodic theory of point transformations and then several advanced topics which are currently undergoing intense research. By selecting one or more of these topics to focus on, the reader can quickly approach the specialized literature and indeed the frontier of the area of interest. Each of the four basic aspects of ergodic theory - examples, convergence theorems, recurrence properties, and entropy - receives first a basic and then a more advanced, particularized treatment. At the introductory level, the book provides clear and complete discussions of the standard examples, the mean and pointwise ergodic theorems, recurrence, ergodicity, weak mixing, strong mixing, and the fundamentals of entropy. Among the advanced topics are a thorough treatment of maximal functions and their usefulness in ergodic theory, analysis, and probability, an introduction to almost-periodic functions and topological dynamics, a proof of the Jewett-Krieger Theorem, an introduction to multiple recurrence and the Szemeredi-Furstenberg Theorem, and the Keane-Smorodinsky proof of Ornstein's Isomorphism Theorem for Bernoulli shifts. The author's easily-readable style combined with the profusion of exercises and references, summaries, historical remarks, and heuristic discussions make this book useful either as a text for graduate students or self-study, or as a reference work for the initiated</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Ergodic theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Ergodentheorie</subfield><subfield code="0">(DE-588)4015246-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Ergodentheorie</subfield><subfield code="0">(DE-588)4015246-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">978-0-521-23632-4</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">978-0-521-38997-6</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/CBO9780511608728</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029349643</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511608728</subfield><subfield code="l">BSB01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511608728</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511608728</subfield><subfield code="l">UBR01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">UBR Einzelkauf (Lückenergänzung CUP Serien 2018)</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043940673 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:14Z |
| institution | BVB |
| isbn | 9780511608728 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349643 |
| oclc_num | 992843327 |
| open_access_boolean | |
| owner | DE-12 DE-92 DE-355 DE-BY-UBR |
| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (xi, 329 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Petersen, Karl Endel 1943- Verfasser (DE-588)14248394X aut Ergodic theory Karl Petersen Cambridge Cambridge University Press 1989 1 Online-Ressource (xi, 329 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 2 Title from publisher's bibliographic system (viewed on 05 Oct 2015) The study of dynamical systems forms a vast and rapidly developing field even when one considers only activity whose methods derive mainly from measure theory and functional analysis. Karl Petersen has written a book which presents the fundamentals of the ergodic theory of point transformations and then several advanced topics which are currently undergoing intense research. By selecting one or more of these topics to focus on, the reader can quickly approach the specialized literature and indeed the frontier of the area of interest. Each of the four basic aspects of ergodic theory - examples, convergence theorems, recurrence properties, and entropy - receives first a basic and then a more advanced, particularized treatment. At the introductory level, the book provides clear and complete discussions of the standard examples, the mean and pointwise ergodic theorems, recurrence, ergodicity, weak mixing, strong mixing, and the fundamentals of entropy. Among the advanced topics are a thorough treatment of maximal functions and their usefulness in ergodic theory, analysis, and probability, an introduction to almost-periodic functions and topological dynamics, a proof of the Jewett-Krieger Theorem, an introduction to multiple recurrence and the Szemeredi-Furstenberg Theorem, and the Keane-Smorodinsky proof of Ornstein's Isomorphism Theorem for Bernoulli shifts. The author's easily-readable style combined with the profusion of exercises and references, summaries, historical remarks, and heuristic discussions make this book useful either as a text for graduate students or self-study, or as a reference work for the initiated Ergodic theory Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-23632-4 Erscheint auch als Druck-Ausgabe 978-0-521-38997-6 https://doi.org/10.1017/CBO9780511608728 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Petersen, Karl Endel 1943- Ergodic theory Ergodic theory Ergodentheorie (DE-588)4015246-7 gnd |
| subject_GND | (DE-588)4015246-7 |
| title | Ergodic theory |
| title_auth | Ergodic theory |
| title_exact_search | Ergodic theory |
| title_full | Ergodic theory Karl Petersen |
| title_fullStr | Ergodic theory Karl Petersen |
| title_full_unstemmed | Ergodic theory Karl Petersen |
| title_short | Ergodic theory |
| title_sort | ergodic theory |
| topic | Ergodic theory Ergodentheorie (DE-588)4015246-7 gnd |
| topic_facet | Ergodic theory Ergodentheorie |
| url | https://doi.org/10.1017/CBO9780511608728 |
| work_keys_str_mv | AT petersenkarlendel ergodictheory |