Differentiable and complex dynamics of several variables:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
1999
|
| Series: | Mathematics and its applications
483 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 338 S. |
| ISBN: | 079235771X |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | IMAGE 1
DIFFERENTIABLE AND COMPLEX
DYNAMICS OF SEVERAL VARIABLES
BY PEI-CHU HU SHANDONG UNIVERSITY, JINAN, CHINA
AND
CHUNG-CHUN YANG THE HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY,
KOWLOON, HONG KONG
KLUWER ACADEMIC PUBLISHERS
DORDRECHT / BOSTON / LONDON
IMAGE 2
CONTENTS
PREFACE VII
1 FATOU-JULIA T Y PE THEORY 1
1.1 HYPERBOLIC FIXED POINTS 1
1.2 ATTRACTIVE AND REPULSIVE FIXED POINTS 4
1.3 NORMALITY 9
1.4 EQUICONTINUITY 17
1.5 LIPSCHITZ CONSTANTS AND JULIA SETS 20
1.6 DEGREE OF MAPPINGS AND JULIA SETS 26
1.7 TOPOLOGICAL ENTROPIES AND JULIA SETS 32
2 ERGODIC T H E O R E MS AND INVARIANT SETS 39
2.1 POINCARE RECURRENCE DOMAINS 39
2.2 NEUMANN DOMAINS 43
2.3 BIRKHOFF DOMAINS 47
2.4 ERGODIC POINTS 50
2.5 REGULAER ERGODIC POINTS 54
2.6 L P -ERGODIC POINTS 58
2.7 L-ERGODIC POINTS 60
3 HYPERBOLICITY IN DIFFERENTIABLE DYNAMICS 63
3.1 NONWANDERING SETS AND CHAIN RECURRENT SETS 63
3.2 MEASURE THEORETIC ENTROPIES 68
3.3 LYAPUNOV EXPONENTS 72
3.4 HYPERBOLIC SETS 78
3.5 NOTES ON HYPERBOLIC SETS 84
3.6 MAPPINGS WITH BOUNDED DISTORTION 89
3.7 HAUSDORFF MEASURE AND METRIC 93
4 SOME TOPICS IN DYNAMICS 99
4.1 PROPERTIES OF HAMILTONIAN SYSTEMS 99
4.2 HAMILTONIAN SYSTEMS NEAR AN EQUILIBRIUM SOLUTION 105
4.3 LINEARIZATION OF EQUATIONS 109
4.4 LINEARIZATION OF MAPPINGS 114
4.5 LP-NORMALITY 122
4.6 LP-EQUICONTINUITY 127
4.7 C R -HYPERBOLICITY 129
IMAGE 3
VI CONTENTS
5 HYPERBOLICITY IN C O M P L EX DYNAMICS 137
5.1 COMPLEX DYNAMICS 137
5.2 SCHWARZ LEMMA 143
5.3 KOBAYASHI HYPERBOLICITY 151
5.4 TAUTNESS AND TIGHTNESS 158
5.5 RELATIONS BETWEEN HYPERBOLICITY AND TAUTNESS 162
5.6 JULIA SETS OF MEROMORPHIC MAPPINGS 166
5.7 A GENERALIZATION OF MARTY S CRITERION 172
6 ITERATION THEORY ON P M 179
6.1 MEROMORPHIC SEIF-MAPPINGS ON P M 179
6.2 FATOU SETS IN P M 184
6.3 PERIODIC POINTS 187
6.4 CLASSIFICATION OF RECURRENT DOMAINS ON P 2 190
6.5 EXCEPTIONAL VARIETIES AND CRITICAL SETS 195
6.6 THE NEWTON S METHOD 197
7 COMPLEX DYNAMICS IN C* 203
7.1 ITERATION THEORY ON DOMAINS OF C* 203
7.2 HOLOMORPHIC SELF-MAPPINGS ON C 208
7.3 THE GROUP AUT(C 2 ) 213
7.4 DYNAMICS IN C 2 218
7.5 BOREL S THEOREM ON C 223
7.6 DYNAMICS OF COMPOSITE MAPPINGS 228
A FOUNDATIONS OF DIFFERENTIABLE DYNAMICS 233
A.L BASIC NOTATIONS IN DIFFERENTIABLE GEOMETRY 233
A.2 DYNAMICAL SYSTEMS 242
A.3 FIXED POINTS AND CYCLES 248
A.4 ORBITS AND INVARIANT SETS 254
A.5 THE ISOMETRIC R-ACTIONS 259
A.6 STABILITY 263
A.7 MEASURE AND INTEGRAL 268
B FOUNDATIONS OF C O M P L EX DYNAMICS 275
B.L COMPLEX STRUCTURES 275
B.2 HERMITIAN STRUCTURES 281
B.3 COMPLEX MANIFOLDS 288
B.4 HAMILTONIAN MANIFOLDS 296
B.5 COMPLEX EUCLIDEAN SPACES C 303
B.6 COMPLEX PROJECTIVE SPACES P M AND TORUS C /R 309
B.7 MEROMORPHIC MAPPINGS AND ORDER FUNCTIONS 312
BIBLIOGRAPHY 319
INDEX 335
|
| any_adam_object | 1 |
| author | Hu, Pei-Chu 1961- Yang, Chung-Chun 1942- |
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| dewey-ones | 515 - Analysis |
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| dewey-search | 515/.94 |
| dewey-sort | 3515 294 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013671704 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:49:56Z |
| institution | BVB |
| isbn | 079235771X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009340538 |
| oclc_num | 41256257 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | IX, 338 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Hu, Pei-Chu 1961- Verfasser (DE-588)131783211 aut Differentiable and complex dynamics of several variables by Pei-Chu Hu and Chung-Chun Yang Dordrecht [u.a.] Kluwer Acad. Publ. 1999 IX, 338 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 483 Differentiable dynamical systems Functions of several complex variables Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 s Mehrere komplexe Variable (DE-588)4169285-8 s DE-604 Yang, Chung-Chun 1942- Verfasser (DE-588)131783238 aut Mathematics and its applications 483 (DE-604)BV008163334 483 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009340538&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hu, Pei-Chu 1961- Yang, Chung-Chun 1942- Differentiable and complex dynamics of several variables Mathematics and its applications Differentiable dynamical systems Functions of several complex variables Differenzierbares dynamisches System (DE-588)4137931-7 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| subject_GND | (DE-588)4137931-7 (DE-588)4169285-8 |
| title | Differentiable and complex dynamics of several variables |
| title_auth | Differentiable and complex dynamics of several variables |
| title_exact_search | Differentiable and complex dynamics of several variables |
| title_full | Differentiable and complex dynamics of several variables by Pei-Chu Hu and Chung-Chun Yang |
| title_fullStr | Differentiable and complex dynamics of several variables by Pei-Chu Hu and Chung-Chun Yang |
| title_full_unstemmed | Differentiable and complex dynamics of several variables by Pei-Chu Hu and Chung-Chun Yang |
| title_short | Differentiable and complex dynamics of several variables |
| title_sort | differentiable and complex dynamics of several variables |
| topic | Differentiable dynamical systems Functions of several complex variables Differenzierbares dynamisches System (DE-588)4137931-7 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| topic_facet | Differentiable dynamical systems Functions of several complex variables Differenzierbares dynamisches System Mehrere komplexe Variable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009340538&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT hupeichu differentiableandcomplexdynamicsofseveralvariables AT yangchungchun differentiableandcomplexdynamicsofseveralvariables |