Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2011
|
| Schriftenreihe: | Lecture notes in mathematics
2036 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | X, 112 S. Ill., graph. Darst. 24 cm |
| ISBN: | 9783642236495 3642236499 9783642236501 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1805145569810710528 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
1 INTRODUCTION 1
2 EXPANDING RANDOM MAPS 5
2.1 INTRODUCTORY EXAMPLES 5
2.2 PRELIMINARIES 8
2.3 EXPANDING RANDOM MAPS 8
2.4 UNIFORMLY EXPANDING RANDOM MAPS 9
2.5 REMARKS ON EXPANDING RANDOM MAPPINGS 10
2.6 VISITING SEQUENCES 11
2.7 SPACES OF CONTINUOUS AND HOLDER FUNCTIONS 12
2.8 TRANSFER OPERATOR 13
2.9 DISTORTION PROPERTIES 14
3 THE RPF-THEOREM 17
3.1 FORMULATION OF THE THEOREMS 17
3.2 FREQUENTLY USED AUXILIARY MEASURABLE FUNCTIONS 19
3.3 TRANSFER DUAL OPERATORS 19
3.4 INVARIANT DENSITY 22
3.5 LEVELS OF POSITIVE CONES OF HOLDER FUNCTIONS 24
3.6 EXPONENTIAL CONVERGENCE OF TRANSFER OPERATORS 27
3.7 EXPONENTIAL DECAY OF CORRELATIONS 31
3.8 UNIQUENESS 32
3.9 PRESSURE FUNCTION 33
3.10 GIBBS PROPERTY 35
3.11 SOME COMMENTS ON UNIFORMLY EXPANDING RANDOM MAPS 37
4 MEASURABILITY, PRESSURE AND GIBBS CONDITION 39
4.1 MEASURABLE EXPANDING RANDOM MAPS 39
4.2 MEASURABILITY 41
4.3 THE EXPECTED PRESSURE 42
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1013868536
DIGITALISIERT DURCH
IMAGE 2
X CONTENTS
4.4 ERGODICITY OF FI 43
4.5 RANDOM COMPACT SUBSETS OF POLISH SPACES 43
5 FRACTAL STRUCTURE OF CONFORMAI EXPANDING RANDOM REPELLERS 47 5.1
BOWEN'S FORMULA 47
5.2 QUASI-DETERMINISTIC AND ESSENTIAL SYSTEMS 51
5.3 RANDOM CANTOR SET 54
6 MULTIFRACTAL ANALYSIS 57
6.1 CONCAVE LEGENDRE TRANSFORM 57
6.2 MULTIFRACTAL SPECTRUM 59
6.3 ANALYTICITY OF THE MULTIFRACTAL SPECTRUM FOR UNIFORMLY EXPANDING
RANDOM MAPS 67
7 EXPANDING IN THE MEAN 69
7.1 DEFINITION OF MAPS EXPANDING IN THE MEAN 69
7.2 ASSOCIATED INDUCED MAP 70
7.3 BACK TO THE ORIGINAL SYSTEM 72
7.4 AN EXAMPLE 73
8 CLASSICAL EXPANDING RANDOM SYSTEMS 75
8.1 DEFINITION OF CLASSICAL EXPANDING RANDOM SYSTEMS 75 8.2 CLASSICAL
CONFORMAI EXPANDING RANDOM SYSTEMS 80
8.3 COMPLEX DYNAMICS AND BRUECK AND BUEGER POLYNOMIAL SYSTEMS 81 8.4
DENKER-GORDIN SYSTEMS 84
8.5 CONFORMAI DG*-SYSTEMS 87
8.6 RANDOM EXPANDING MAPS ON SMOOTH MANIFOLD 89
8.7 TOPOLOGICAL EXACTNESS 89
8.8 STATIONARY MEASURES 90
9 REAL ANALYTICITY OF PRESSURE 93
9. 1 THE PRESSURE AS A FUNCTION OF A PARAMETER 93
9.2 REAL CONES 97
9.3 CANONICAL COMPLEXIFICATION 100
9.4 THE PRESSURE IS REAL-ANALYTIC 103
9.5 DERIVATIVE OF THE PRESSURE 106
REFERENCES 109
INDEX I LL |
| any_adam_object | 1 |
| author | Mayer, Volker 1964- Skorulski, Bartlomiej Urbański, Mariusz 1958- |
| author_GND | (DE-588)140755519 (DE-588)1018502971 (DE-588)120432684 |
| author_facet | Mayer, Volker 1964- Skorulski, Bartlomiej Urbański, Mariusz 1958- |
| author_role | aut aut aut |
| author_sort | Mayer, Volker 1964- |
| author_variant | v m vm b s bs m u mu |
| building | Verbundindex |
| bvnumber | BV039709339 |
| classification_rvk | SI 850 |
| classification_tum | MAT 344f MAT 280f |
| ctrlnum | (OCoLC)744297266 (DE-599)DNB1013868536 |
| dewey-full | 515.39 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.39 |
| dewey-search | 515.39 |
| dewey-sort | 3515.39 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV039709339 |
| illustrated | Illustrated |
| indexdate | 2024-07-21T00:16:07Z |
| institution | BVB |
| isbn | 9783642236495 3642236499 9783642236501 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024557721 |
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| owner_facet | DE-91G DE-BY-TUM DE-824 DE-83 DE-188 DE-11 |
| physical | X, 112 S. Ill., graph. Darst. 24 cm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Mayer, Volker 1964- Verfasser (DE-588)140755519 aut Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry Volker Mayer ; Bartlomiej Skorulski ; Mariusz Urbanski Berlin [u.a.] Springer 2011 X, 112 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2036 Literaturangaben Dimensionsspektrum (DE-588)4808937-0 gnd rswk-swf Zufälliges dynamisches System (DE-588)4335207-8 gnd rswk-swf Hausdorff-Dimension (DE-588)4159234-7 gnd rswk-swf Zufälliges dynamisches System (DE-588)4335207-8 s Hausdorff-Dimension (DE-588)4159234-7 s Dimensionsspektrum (DE-588)4808937-0 s DE-604 Skorulski, Bartlomiej Verfasser (DE-588)1018502971 aut Urbański, Mariusz 1958- Verfasser (DE-588)120432684 aut Erscheint auch als Online-Ausgabe Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry Lecture notes in mathematics 2036 (DE-604)BV000676446 2036 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3859667&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024557721&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mayer, Volker 1964- Skorulski, Bartlomiej Urbański, Mariusz 1958- Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry Lecture notes in mathematics Dimensionsspektrum (DE-588)4808937-0 gnd Zufälliges dynamisches System (DE-588)4335207-8 gnd Hausdorff-Dimension (DE-588)4159234-7 gnd |
| subject_GND | (DE-588)4808937-0 (DE-588)4335207-8 (DE-588)4159234-7 |
| title | Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry |
| title_auth | Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry |
| title_exact_search | Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry |
| title_full | Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry Volker Mayer ; Bartlomiej Skorulski ; Mariusz Urbanski |
| title_fullStr | Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry Volker Mayer ; Bartlomiej Skorulski ; Mariusz Urbanski |
| title_full_unstemmed | Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry Volker Mayer ; Bartlomiej Skorulski ; Mariusz Urbanski |
| title_short | Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry |
| title_sort | distance expanding random mappings thermodynamical formalism gibbs measures and fractal geometry |
| topic | Dimensionsspektrum (DE-588)4808937-0 gnd Zufälliges dynamisches System (DE-588)4335207-8 gnd Hausdorff-Dimension (DE-588)4159234-7 gnd |
| topic_facet | Dimensionsspektrum Zufälliges dynamisches System Hausdorff-Dimension |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3859667&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024557721&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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