Infinite ergodic theory of numbers:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
De Gruyter
[2016]
|
| Series: | De Gruyter Graduate
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 191 Seiten Diagramme |
| ISBN: | 9783110439410 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
MATHEMATICAL SYMBOLS * IX
1 NUMBER-THEORETICAL DYNAMICAL SYSTEMS * 1
1.1 CONTINUED FRACTIONS AND DIOPHANTINE APPROXIMATION * 1
1.1.1 CONTINUED FRACTIONS * 1
1.1.2 ELEMENTARY DIOPHANTINE APPROXIMATION: HURWITZ*S THEOREM AND BADLY
APPROXIMATE NUMBERS * 7
1.2 TOPOLOGICAL DYNAMICAL SYSTEMS * 12
1.2.1 THE GAUSS MAP * 15
1.2.2 SYMBOLIC DYNAMICS * 16
1.2.3 A RETURN TO THE GAUSS MAP * 19
1.2.4 ELEMENTARY METRICAL DIOPHANTINE ANALYSIS * 21
1.2.5 MARKOV PARTITIONS FOR INTERVAL MAPS * 26
1.3 THE FAREY MAP: DEFINITION AND TOPOLOGICAL PROPERTIES * 30
1.3.1 THE FAREY MAP * 30
1.3.2 TOPOLOGICAL PROPERTIES OF THE FAREY MAP * 34
1.4 TWO FURTHER EXAMPLES * 40
1.4.1 THE A-I.ILROTH MAPS * 40
1.4.2 THE A-FAREY MAPS * 44
1.4.3 TOPOLOGICAL PROPERTIES OF
FA
* 48
1.4.4 EXPANDING AND EXPANSIVE PARTITIONS * 51
1.4.5 METRICAL DIOPHANTINE-LIKE RESULTS FOR THE O-LUROTH EXPANSION * 53
1.5 NOTES AND HISTORICAL REMARKS * 58
1.5.1 THE FAREY SEQUENCE * 58
1.5.2 THE CLASSICAL LIIROTH SERIES * 59
1.6 EXERCISES
-----
61
2 BASIC ERGODIC THEORY * 64
2.1 INVARIANT MEASURES * 64
2.1.1 INVARIANT MEASURES FOR THE GAUSS AND O-LUEROTH SYSTEM * 66
2.2 RECURRENCE AND CONSERVATIVE * 69
2.3 THE TRANSFER OPERATOR * 75
2.3.1 JACOBIANS AND THE CHANGE OF VARIABLE FORMULA * 75
2.3.2 OBTAINING INVARIANT MEASURES VIA THE TRANSFER OPERATOR * 76
2.3.3 THE RUELLE OPERATOR * 79
2.3.4 INVARIANT MEASURES FOR
F,FA,G
AND
LA
* 82
2.3.5 INVARIANT MEASURES VIA THE JUMP TRANSFORMATION * 86
2.4
2
.
4.1
2.4.2
2
.
4.3
2
.
4.4
2
.
4.5
2
.
4.6
2.5
2.6
3
3.1
3.2
3.2.1
3.2.2
3.3
4
4.1
4.2
4.3
4.4
5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
ERGODICITY AND EXACTNESS
-----
88
ERGODICITY OF THE SYSTEMS
6
AND
LA
-----
92
ERGODIC THEOREMS FOR PROBABILITY SPACES AND CONSEQUENCES FOR THE
GAUSS AND CR-LUEROTH SYSTEMS
-----
96
ERGODIC THEOREMS FOR INFINITE MEASURES * 103
INDUCING
-----
105
UNIQUENESS OF THE INVARIANT MEASURES FOR FAND
FA
* 109
PROOF OF HOPF*S RATIO ERGODIC THEOREM * 112
EXACTNESS REVISITED
-----
115
EXERCISES
-----
120
RENEWAL THEORY AND A-SUM-LEVEL SETS * 122
SUM-LEVEL SETS
-----
122
SUM-LEVEL SETS FOR THE CR-LUEROTH EXPANSION * 123
CLASSICAL RENEWAL RESULTS
-----
124
RENEWAL THEORY APPLIED TO THE A-SUM-LEVEL SETS * 132
EXERCISES * 135
INFINITE ERGODIC THEORY * 137
THE FUNCTIONAL ANALYTIC PERSPECTIVE AND THE CHACON-ORNSTEIN
ERGODIC THEOREM * 137
POINTWISE DUAL ERGODICITY
-----
147
^-MIXING, DARLING-KAC SETS AND POINTWISE DUAL ERGODICITY * 151
EXERCISES * 157
APPLICATIONS OF INFINITE ERGODIC THEORY * 159
SUM-LEVEL SETS FOR THE CONTINUED FRACTION EXPANSION,
FIRST INVESTIGATIONS * 159
(//-MIXING FOR THE GAUSS MAP AND THE GAUSS PROBLEM * 161
POINTWISE DUAL ERGODICITY FOR THE FAREY MAP * 167
UNIFORM AND UNIFORMLY RETURNING SETS * 168
FINER ASYMPTOTICS OF LEBESGUE MEASURE OF SUM-LEVEL SETS * 173
UNIFORM DISTRIBUTION OF THE EVEN STERN-BROCOT SEQUENCE * 177
EXERCISES * 181
BIBLIOGRAPHY
-----
183
|
| any_adam_object | 1 |
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| author_role | aut aut aut |
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| building | Verbundindex |
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| ctrlnum | (OCoLC)965117183 (DE-599)DNB1076282598 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:31:59Z |
| institution | BVB |
| isbn | 9783110439410 |
| language | English |
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| physical | XIII, 191 Seiten Diagramme |
| publishDate | 2016 |
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| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter Graduate |
| spelling | Kesseböhmer, Marc Verfasser aut Infinite ergodic theory of numbers Marc Kesseböhmer, Sara Munday, Bernd Otto Stratmann Berlin De Gruyter [2016] XIII, 191 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier De Gruyter Graduate Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Fachhochschul-/Hochschulausbildung Ergodentheorie (DE-588)4015246-7 s Zahlentheorie (DE-588)4067277-3 s DE-604 Munday, Sara Verfasser (DE-588)1116447908 aut Stratmann, Bernd O. 1957-2015 Verfasser (DE-588)132923610 aut Erscheini auch als Online-Ausgabe, EPUB 978-3-11-043085-1 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029080716&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kesseböhmer, Marc Munday, Sara Stratmann, Bernd O. 1957-2015 Infinite ergodic theory of numbers Ergodentheorie (DE-588)4015246-7 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4015246-7 (DE-588)4067277-3 |
| title | Infinite ergodic theory of numbers |
| title_auth | Infinite ergodic theory of numbers |
| title_exact_search | Infinite ergodic theory of numbers |
| title_full | Infinite ergodic theory of numbers Marc Kesseböhmer, Sara Munday, Bernd Otto Stratmann |
| title_fullStr | Infinite ergodic theory of numbers Marc Kesseböhmer, Sara Munday, Bernd Otto Stratmann |
| title_full_unstemmed | Infinite ergodic theory of numbers Marc Kesseböhmer, Sara Munday, Bernd Otto Stratmann |
| title_short | Infinite ergodic theory of numbers |
| title_sort | infinite ergodic theory of numbers |
| topic | Ergodentheorie (DE-588)4015246-7 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Ergodentheorie Zahlentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029080716&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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