Verfügbarkeit: Infinite ergodic theory of numbers | Technische Universität München

Infinite ergodic theory of numbers:

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Bibliographische Detailangaben
Beteiligte Personen:	Kesseböhmer, Marc (VerfasserIn), Munday, Sara (VerfasserIn), Stratmann, Bernd O. 1957-2015 (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin De Gruyter [2016]
Schriftenreihe:	De Gruyter Graduate
Schlagwörter:	Ergodentheorie Zahlentheorie Fachhochschul-/Hochschulausbildung
Links:	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
Umfang:	XIII, 191 Seiten Diagramme
ISBN:	9783110439410

Internformat

MARC


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Datensatz im Suchindex

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DE-BY-TUM_katkey	2237269
DE-BY-TUM_location	01
DE-BY-TUM_media_number	040008017638
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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: HURWITZS 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 HOPFS 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
author	Kesseböhmer, Marc Munday, Sara Stratmann, Bernd O. 1957-2015
author_GND	(DE-588)1116447908 (DE-588)132923610
author_facet	Kesseböhmer, Marc Munday, Sara Stratmann, Bernd O. 1957-2015
author_role	aut aut aut
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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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id	DE-604.BV043667481
illustrated	Not Illustrated
indexdate	2024-12-20T17:42:04Z
institution	BVB
isbn	9783110439410
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-029080716
oclc_num	965117183
open_access_boolean
owner	DE-703 DE-29T DE-83 DE-91G DE-BY-TUM DE-384
owner_facet	DE-703 DE-29T DE-83 DE-91G DE-BY-TUM DE-384
physical	XIII, 191 Seiten Diagramme
publishDate	2016
publishDateSearch	2016
publishDateSort	2016
publisher	De Gruyter
record_format	marc
series2	De Gruyter Graduate
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
work_keys_str_mv	AT kessebohmermarc infiniteergodictheoryofnumbers AT mundaysara infiniteergodictheoryofnumbers AT stratmannberndo infiniteergodictheoryofnumbers

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