Fine Structures of Hyperbolic Diffeomorphisms:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Springer Berlin
2008
|
| Ausgabe: | 1. Ed. |
| Schriftenreihe: | Springer Monographs in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=2646069&custom_att_2=simple_viewer Inhaltsverzeichnis |
| Beschreibung: | XVI, 353 S. graph. Darst. |
| ISBN: | 9783540875246 |
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| 100 | 1 | |a Pinto, Alberto A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fine Structures of Hyperbolic Diffeomorphisms |c Alberto A. Pinto ; David A. Rand ; Flávio Ferreira |
| 250 | |a 1. Ed. | ||
| 264 | 1 | |a Berlin |b Springer Berlin |c 2008 | |
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| 700 | 1 | |a Rand, David A. |e Verfasser |0 (DE-588)114855331 |4 aut | |
| 700 | 1 | |a Ferreira, Flávio |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804142701623377920 |
|---|---|
| adam_text | CONTENTS
INTRODUCTION 1
1.1
STABLE AND UNSTABLE LEAVES 1
1.2 MARKING 3
1.3 METRIC 4
1.4 INTERVAL NOTATION 5
1.5 BASIC HOLONOMIES 6
1.6 FOLIATED ATLAS 6
1.7 FOLIATED ATLAS
A
L
(G,P)
8
1.8 STRAIGHTENED GRAPH-LIKE CHARTS 10
1.9 ORTHOGONAL ATLAS 17
1.10 FURTHER LITERATURE 19
H
R
STRUCTURE
S
21
2.1 CONJUGACIES 21
2.2 HR - HOLDER RATIOS 22
2.3 FOLIATED ATLAS
A{R)
23
2.4 INVARIANTS 25
2.5 HR ORTHOGONAL ATLAS 27
2.6 COMPLETE INVARIANT 28
2.7 MODULI SPACE 33
2.8 FURTHER LITERATURE 36
SOLENOI
D FUNCTION
S
37
3.1 REALIZED SOLENOID FUNCTIONS 37
3.2 HOLDER CONTINUITY 38
3.3 MATCHING CONDITION 38
3.4 BOUNDARY CONDITION 39
3.5 SCALING FUNCTION 40
3.6 CYLINDER-GAP CONDITION 41
3.7 SOLENOID FUNCTIONS 41
3.8 FURTHER LITERATURE 43
GESCANNT DURCH
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/989960528
DIGITALISIERT DURCH
XII CONTENTS
4 SELF-RENORMALIZABL
E STRUCTURE
S
45
4.1 TRAIN-TRACK
S 45
4.2 CHART
S 47
4.3 MARKOV MAP
S 47
4.4 EXCHANGE PSEUDO-GROUPS 48
4.5 MARKINGS 49
4.6 SELF-RENORMALIZABLE STRUCTURE
S 51
4.7 HYPERBOLIC DIFFEOMORPHISMS 52
4.8 EXPLOSION OF SMOOTHNESS 52
4.9 FURTHE
R LITERATUR
E 53
5 RIGIDIT
Y
55
5.1 COMPLETE SETS OF HOLONOMIES 55
5.2 C
1
1
DIFFEOMORPHISMS 58
5.3
C
L
H
L
AN
D CROSS-RATIO DISTORTION
S FOR RATI
O FUNCTIONS 59
5.4 FUNDAMENTA
L RIGIDITY LEMMA 62
5.5 EXISTENCE OF AFFINE MODEIS 65
5.6 PROOF OF TH
E HYPERBOLIC AN
D ANOSOV RIGIDITY 67
5.7 TWIN LEAVES FOR CODIMENSION 1 ATTRACTOR
S 68
5.8 NON-EXISTENCE OF AFFINE MODEIS 70
5.9 NON-EXISTENCE OF UNIFORMLY
C
L
HD
COMPLETE SETS OF
HOLONOMIES FOR CODIMENSION 1 ATTRACTOR
S 71
5.10 FURTHE
R LITERATUR
E 72
6 GIBB
S MEASURE
S
73
6.1 DUAL SYMBOLIC SETS 73
6.2 WEIGHTED SCALING FUNCTION AN
D JACOBIA
N 74
6.3 WEIGHTED RATI
O STRUCTUR
E 75
6.4 GIBBS MEASURE AN
D IT
S DUA
L 76
6.5 FURTHE
R LITERATUR
E 84
7 MEASUR
E SCALIN
G FUNCTION
S
85
7.1 GIBBS MEASURES 85
7.2 EXTENDED MEASURE SCALING FUNCTION 86
7.3 FURTHE
R LITERATUR
E 92
8 MEASUR
E SOLENOI
D FUNCTION
S
;.
. .
. 93
8.1 MEASURE SOLENOID FUNCTIONS 93
8.1.1 CYLINDER-CYLINDER CONDITION 94
8.2 MEASURE RATI
O FUNCTIONS 95
8.3 NATURA
L GEOMETRIC MEASURES 96
8.4 MEASURE RATI
O FUNCTIONS AN
D SELF-RENORMALIZABLE STRUCTURE
S ...
. 99
8.5 DUAL MEASURE RATI
O FUNCTION 104
8.6 FURTHE
R LITERATUR
E 106
CONTENTS
XIII
9 COCYCLE-GA
P PAIR
S
107
9.1 MEASURE-LENGTH RATI
O COCYCLE 107
9.2 GA
P RATI
O FUNCTION 109
9.3 RATI
O FUNCTIONS 109
9.4 COCYCLE-GAP PAIR
S 111
9.5 FURTHE
R LITERATUR
E 117
1
0 HAUSDORF
F REALIZATION
S
119
10.1 ONE-DIMENSIONAL REALIZATIONS OF GIBBS MEASURES 119
10.2 TWO-DIMENSIONAL REALIZATIONS OF GIBBS MEASURES 122
10.3 INVARIANT HAUSDORFF MEASURES 127
10.3.1 MODULI SPACE
SOC
131
10.3.2 MODULI SPACE OF COCYCLE-GAP PAIR
S 132
10.3.3 5
T
-BOUNDED SOLENOID EQUIVALENCE CLASS OF GIBBS MEASURES 132
10.4 FURTHE
R LITERATUR
E 134
1
1 EXTENDE
D LIVSIC-SINA
I EIGENVALU
E FORMUL
A
135
11.1 EXTENDIN
G TH
E EIGENVALUES S RESULT OF DE LA LLAVE, MARCO AN
D
MORIYON 135
11.2 EXTENDIN
G TH
E EIGENVALUE FORMULA OF A. N
. LIVSIC AN
D JA
. G.
SINAI 140
11.3 FURTHE
R LITERATUR
E 141
1
2 AR
E EXCHANG
E SYSTEM
S AN
D RENORMALIZATIO
N
143
12.1 ARE EXCHANGE SYSTEMS 143
12.1.1 INDUCED ARC EXCHANGE SYSTEMS 145
12.2 RENORMALIZATION OF ARC EXCHANGE SYSTEMS 148
12.2.1 RENORMALIZATION OF INDUCED ARC EXCHANGE SYSTEMS 150
12.3 MARKOV MAPS VERSUS RENORMALIZATION 152
12.4
C
1+H
FLEXIBILITY 155
12.5
C
L
HD
RIGIDITY 156
12.6 FURTHE
R LITERATUR
E 159
1
3 GOLDE
N TILING
S (I
N COLLABORATIO
N WIT
H J.P
. ALMEID
A AN
D
A
. PORTELA
)
161
13.1 GOLDEN DIFEOMORPHISMS 161
13.1.1 GOLDEN TRAIN-TRAC
K 162
13.1.2 GOLDEN ARC EXCHANGE SYSTEMS 163
13.1.3 GOLDEN RENORMALIZATION 165
13.1.4 GOLDEN MARKOV MAPS 167
13.2 ANOSOV DIFFEOMORPHISMS 168
13.2.1 GOLDEN DIFFEOMORPHISMS 169
13.2.2 ARC EXCHANGE SYSTEM 170
13.2.3 MARKOV MAP
S 172
13.2.4 EXCHANGE PSEUDO-GROUPS 173
XIV CONTENTS
13.2.5 SELF-RENORMALIZABLE STRUCTURE
S 174
13.3 HR STRUCTURE
S 174
13.4 FIBONACCI DECOMPOSITION 175
13.4.1 MATCHIN
G CONDITION 176
13.4.2 BOUNDAR
Y CONDITION 176
13.4.3 TH
E EXPONENTIALLY FAST FIBONACCI REPETITIV
E PROPERT
Y ..
. 177
13.4.4 GOLDEN TILINGS 177
13.4.5 GOLDEN TILINGS VERSUS SOLENOID FUNCTIONS 178
13.4.6 GOLDEN TILINGS VERSUS ANOSOV DIFFEOMORPHISMS 181
13.5 FURTHE
R LITERATUR
E 182
1
4 PSEUDO-ANOSO
V DIFFEOMORPHISM
S I
N PSEUDO-SURFACE
S
183
14.1 AFFINE PSEUDO-ANOSOV MAP
S 183
14.2 PAPE
R MODEIS
S
K
184
14.3 PSEUDO-LINEAR ALGEBRA 186
14.4 PSEUDO-DIFFERENTIABLE MAPS 191
14.4.1
C
R
PSEUDO-MANIFOLDS 194
14.4.2 PSEUDO-TANGEN
T SPACES 195
14.4.3 PSEUDO-INNER PRODUC
T ON
EK
195
14.5
C
R
FOLIATIONS 198
14.6 FURTHE
R LITERATUR
E 199
A APPENDIX A: CLASSIFYING C
1
+
STRUCTURES ON THE REAL LINE
..
. 201
A.
L TH
E GRID 201
A.2 CROSS-RATIO DISTORTIO
N OF GRIDS 202
A.3 QUASISYMMETRIC HOMEOMORPHISMS 204
A.4 HORIZONTAL AN
D VERTICAL TRANSLATION
S OF RATI
O DISTORTION
S 207
A.5 UNIFORMLY ASYMPTOTICALLY AFFINE (UAA) HOMEOMORPHISMS 214
A.6 C
1+
R
DIFFEOMORPHISMS 224
A.7
C
2+R
DIFFEOMORPHISMS 228
A.8 CROSS-RATIO DISTORTIO
N AN
D SMOOTHNESS 232
A.9 FURTHER LITERATUR
E 233
B APPENDI
X B
: CLASSIFYIN
G C
1
+
STRUCTURE
S O
N CANTO
R SETS
...
. 23
5
B.
L SMOOTH STRUCTURE
S ON TREES 235
B.L.
L EXAMPLES 236
B.2 BASIC DEFINITIONS 239
B.3 (1 -+- A)-CONTAC
T EQUIVALENCE 240
B.3.1 (1 +
Q
)
SCALE AN
D CONTACT EQUIVALENCE 241
B.3.2 A REFINEMENT OF TH
E EQUIVALENCE PROPERT
Y 242
B.3.3 TH
E MA
P
L
T
243
B.3.4 TH
E DEFINITION OF TH
E CONTAC
T AN
D GAP MAPS 246
B.3.5 TH
E MA
P
L
N
247
B.3.6 TH
E SEQUENCE OF MAPS
L
N
CONVERGE 247
B.3.7 TH
E MA
P
L
X
251
CONTENTS XV
B.3.8 SUFFICIENT CONDITION FOR C
1+A
~-EQUIVALEN
T 252
B.3.9 NECESSARY CONDITION FOR
C
1+A
-EQUIVALENT 252
B.4 SMOOT
H STRUCTURE
S WIT
H A-CONTROLLED GEOMETRY AND BOUNDED
GEOMETRY 254
B.4.1 BOUNDED GEOMETRY 257
B.5 FURTHE
R LITERATUR
E 259
C APPENDI
X C
: EXPANDIN
G DYNAMIC
S O
F TH
E CIRCL
E
261
C.
L
C
1+HOELDER
STRUCTURE
S
U
FOR TH
E EXPANDING CIRCLE MA
P
E
261
C.2 SOLENOIDS (E,S) 263
C.3 SOLENOID FUNCTIONS
S : C -^ R
+
265
C.4 D-ADIC TILINGS AN
D GRIDS 267
C.5 SOLENOIDAL CHART
S FOR TH
E
C
1+HOELDER
EXPANDING CIRCLE MA
P
E...
269
C.6 SMOOTH PROPERTIES OF SOLENOIDAL CHART
S 271
C.7 A TEICHMUELLER SPACE 272
C.8 SULLIVAN S SOLENOIDAL SURFACES 273
C.9 (UAA) STRUCTURE
S
U
FOR TH
E EXPANDING CIRCLE MAP
E
274
CI
O REGULARITIES OF TH
E SOLENOIDAL CHART
S 275
C.L
L FURTHE
R LITERATUR
E 277
D APPENDI
X D
: MARKO
V MAP
S O
N TRAIN-TRACK
S
279
D.
L
COOKIE-CUTTERS 279
D.2 PRONGE
D SINGULARITIES IN PSEUDO-ANOSOV MAPS 280
D.3 TRAIN-TRACK
S 281
D.3.1 TRAIN-TRACK OBTAINE
D BY GLUEING 282
D.4 MARKOV MAPS 283
D.5 TH
E SCALING FUNCTION 286
D.5.1 A HOLDER SCALING FUNCTION WITHOUT A CORRESPONDING
SMOOTH MARKOV MA
P 290
D.6 SMOOTHNESS OF MARKOV MAPS AN
D GEOMETRY OF TH
E CYLINDER
STRUCTURE
S 291
D.6.1 SOLENOID SET 291
D.6.2 PRE-SOLENOID FUNCTIONS 292
D.6.3 TH
E SOLENOID PROPERT
Y OF A CYLINDER STRUCTUR
E 293
D.6.4 TH
E SOLENOID EQUIVALENCE BETWEEN CYLINDER STRUCTURES..
. 295
D.7 SOLENOID FUNCTIONS 297
D.7.1 TURNTABL
E CONDITION 298
D.7.2 MATCHING CONDITION 298
D.8 EXAMPLE
S OF SOLENOID FUNCTIONS FOR MARKOV MAPS 299
D.8.1 TH
E HOROCYCLE MAPS AND TH
E DIFFEOMORPHISMS OF TH
E
CIRCLE 300
D.8.2 CONNECTIONS OF A SMOOT
H MARKOV MA
P 301
D.9 Q-SOLENOID FUNCTIONS 302
D.10 CANONICAL SET C OF CHART
S 303
D.L
L ONE-TO-ONE CORRESPONDENCES 305
XVI CONTENTS
D.12 EXISTENCE OF EIGENVALUES FOR (UAA) MARKOV MAP
S 307
D.13 FURTHE
R LITERATUR
E 311
E APPENDI
X E: EXPLOSION OF SMOOTHNESS FOR MARKOV FAMILIES
. 313
E.
L MARKOV FAMILIES ON TRAIN-TRACK
S 313
E.L.
L TRAIN-TRACK
S 313
E.1.2 MARKOV FAMILIES 314
E.1.3 (UAA) MARKOV FAMILIES 315
E.1.4 BOUNDE
D GEOMETR
Y 318
E.2 (UAA) CONJUGACIES 319
E.3 CANONICAL CHART
S 324
E.4 SMOOT
H BOUND
S FOR
C
R
MARKOV FAMILIES 325
E.4.1 ARZELAE-ASCOLI THEORE
M 330
E.5 SMOOT
H CONJUGACIES 331
E.6 FURTHE
R LITERATUR
E 334
REFERENCES
335
INDEX
347
|
| any_adam_object | 1 |
| author | Pinto, Alberto A. Rand, David A. Ferreira, Flávio |
| author_GND | (DE-588)114855331 |
| author_facet | Pinto, Alberto A. Rand, David A. Ferreira, Flávio |
| author_role | aut aut aut |
| author_sort | Pinto, Alberto A. |
| author_variant | a a p aa aap d a r da dar f f ff |
| building | Verbundindex |
| bvnumber | BV025524997 |
| classification_rvk | SK 810 |
| ctrlnum | (OCoLC)271643833 (DE-599)BVBBV025524997 |
| 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 |
| edition | 1. Ed. |
| format | Book |
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| id | DE-604.BV025524997 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:35:57Z |
| institution | BVB |
| isbn | 9783540875246 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020132711 |
| oclc_num | 271643833 |
| open_access_boolean | |
| owner | DE-11 |
| owner_facet | DE-11 |
| physical | XVI, 353 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer Berlin |
| record_format | marc |
| series2 | Springer Monographs in Mathematics |
| spelling | Pinto, Alberto A. Verfasser aut Fine Structures of Hyperbolic Diffeomorphisms Alberto A. Pinto ; David A. Rand ; Flávio Ferreira 1. Ed. Berlin Springer Berlin 2008 XVI, 353 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer Monographs in Mathematics Diffeomorphismus (DE-588)4149767-3 gnd rswk-swf Hyperbolizität (DE-588)4710615-3 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Diffeomorphismus (DE-588)4149767-3 s Hyperbolizität (DE-588)4710615-3 s DE-604 Rand, David A. Verfasser (DE-588)114855331 aut Ferreira, Flávio Verfasser aut http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=2646069&custom_att_2=simple_viewer Verlagsdaten Springer DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020132711&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pinto, Alberto A. Rand, David A. Ferreira, Flávio Fine Structures of Hyperbolic Diffeomorphisms Diffeomorphismus (DE-588)4149767-3 gnd Hyperbolizität (DE-588)4710615-3 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4149767-3 (DE-588)4710615-3 (DE-588)4013396-5 |
| title | Fine Structures of Hyperbolic Diffeomorphisms |
| title_auth | Fine Structures of Hyperbolic Diffeomorphisms |
| title_exact_search | Fine Structures of Hyperbolic Diffeomorphisms |
| title_full | Fine Structures of Hyperbolic Diffeomorphisms Alberto A. Pinto ; David A. Rand ; Flávio Ferreira |
| title_fullStr | Fine Structures of Hyperbolic Diffeomorphisms Alberto A. Pinto ; David A. Rand ; Flávio Ferreira |
| title_full_unstemmed | Fine Structures of Hyperbolic Diffeomorphisms Alberto A. Pinto ; David A. Rand ; Flávio Ferreira |
| title_short | Fine Structures of Hyperbolic Diffeomorphisms |
| title_sort | fine structures of hyperbolic diffeomorphisms |
| topic | Diffeomorphismus (DE-588)4149767-3 gnd Hyperbolizität (DE-588)4710615-3 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Diffeomorphismus Hyperbolizität Dynamisches System |
| url | http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=2646069&custom_att_2=simple_viewer http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020132711&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT pintoalbertoa finestructuresofhyperbolicdiffeomorphisms AT randdavida finestructuresofhyperbolicdiffeomorphisms AT ferreiraflavio finestructuresofhyperbolicdiffeomorphisms |