Fixed point theorems and their applications:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2013
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XI, 234 S. graph. Darst. |
| ISBN: | 9789814458917 |
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MARC
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| 245 | 1 | 0 | |a Fixed point theorems and their applications |c Ioannis Farmakis ; Martin Moskowitz |
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| 300 | |a XI, 234 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
| _version_ | 1804150557612441600 |
|---|---|
| adam_text | Contents
Preface
and Acknowledgments
ix
Introduction
1
1
Early Fixed Point Theorems
3
1.1
The Picard-Banach Theorem
............... 3
1.2
Vector Fields on Spheres
.................. 5
1.3
Proof of the
Brouwer
Theorem and Corollaries
..... 9
1.3.1
A Counter Example
................ 12
1.3.2
Applications of the
Brouwer
Theorem
...... 15
1.3.3
The Perron-Frobenius Theorem
.......... 16
1.3.4
Google; A Billion Dollar Fixed Point Theorem
. . 21
1.4
Fixed Point Theorems for Groups of
Affine
Maps of
Шп
24
1.4.1 Affine
Maps and Actions
.............. 25
1.4.2 Affine
Actions of
Non
Compact Groups
...... 30
2
Fixed Point Theorems in Analysis
35
2.1
The
Schaüder-Tychonoff
Theorem
............ 36
2.1.1
Proof of the
Schaüder-Tychonoff
Theorem
.... 38
2.2
Applications of the
Schaüder-Tychonoff
Theorem
.... 43
2.3
The Theorems of
Hahn, Kakutani
and Markov-Kakutani
46
2.4
Amenable Groups
..................... 51
2.4.1
Amenable Groups
.................. 52
2.4.2
Structure of Connected Amenable Lie Groups
. . 54
vi
Contents
3
The Lefschetz Fixed Point Theorem
57
3.1
The Lefschetz Theorem for Compact Polyhedra
..... 58
3.1.1
Projective
Spaces
.................. 62
3.2
The Lefschetz Theorem for a Compact Manifold
.... 64
3.2.1
Preliminaries from Differential Topology
..... 64
3.2.2
Transversality
.................... 67
3.3
Proof of the Lefschetz Theorem
.............. 76
3.4
Some Applications
..................... 81
3.4.1
Maximal Tori in Compact Lie Groups
...... 83
3.4.2
The
Poincaré-Hopf s
Index Theorem
....... 87
3.5
The Atiyah-Bott Fixed Point Theorem
.......... 94
3.5.1
The Case of the
de
Rham Complex
........ 104
4
Fixed Point Theorems in Geometry
109
4.1
Some Generalities on Riemannian Manifolds
....... 110
4.2
Hadamard
Manifolds and Cartan s Theorem
....... 124
4.3
Fixed Point Theorems for Compact Manifolds
...... 135
5
Fixed Points of Volume Preserving Maps
143
5.1
The
Poincaré
Recurrence Theorem
............ 143
5.2
Symplectic Geometry and its Fixed Point Theorems
. . 146
5.2.1
Introduction to Symplectic Geometry
....... 146
5.2.2
Fixed Points of Symplectomorphisms
....... 153
5.2.3
Arnold s Conjecture
................ 154
5.3
Poincaré s
Last Geometric Theorem
........... 155
5.4
Automorphisms of Lie Algebras
.............. 163
5.5
Hyperbolic Automorphisms of a Manifold
........ 167
5.5.1
The Case of a Torus
................ 169
5.5.2
Anosov Diffeomorphisms
.............. 173
5.5.3
Nilmanifold Examples of Anosov Diffeomorphisms
177
5.6
The Lefschetz
Zeta
Function
............... 179
6
Borel s Fixed Point Theorem in Algebraic Groups
187
6.1
Complete Varieties and Borel s Theorem
......... 187
6.2
The
Projective
and
Grassmann
Spaces
.......... 190
6.3
Projective
Varieties
..................... 193
Contents
vii
6.4
Consequences of
Boreľs
Fixed Point Theorem
...... 197
6.5
Two Conjugacy Theorems for Real Linear Lie Groups
. 200
7
Miscellaneous Fixed Point Theorems
203
7.1
Applications to Number Theory
.............. 203
7.1.1
The Little
Fermat
Theorem
............ 203
7.1.2
Fermat
s
Two Squares Theorem
.......... 205
7.2
Fixed Points in Group Theory
............... 207
7.3
A Fixed Point Theorem in Complex Analysis
...... 209
8
A Fixed Point Theorem in Set Theory
211
Afterword
217
Bibliography
219
Index
229
FIXED
POINT THEOREMS RND
THEIR flPPLICRTIONS
.is is the only book that deals comprehensively
with fixed point theorems throughout
mathematics.Their importance is due, as the book
demonstrates, to their wide applicability. Beyond
the first chapter each of the other seven can be read
independently of the others so the reader has much
flexibility to follow his/her own interests. The book
is written for graduate students and professional
mathematicians and could be of interest to
physicists, economists and engineers.
|
| any_adam_object | 1 |
| author | Farmakis, Ioannis Moskowitz, Martin A. |
| author_GND | (DE-588)1043300783 (DE-588)114556628 |
| author_facet | Farmakis, Ioannis Moskowitz, Martin A. |
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| author_sort | Farmakis, Ioannis |
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| building | Verbundindex |
| bvnumber | BV041154136 |
| classification_rvk | SK 110 |
| ctrlnum | (OCoLC)869848912 (DE-599)HBZHT017704203 |
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| id | DE-604.BV041154136 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:40:49Z |
| institution | BVB |
| isbn | 9789814458917 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026129545 |
| oclc_num | 869848912 |
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| physical | XI, 234 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Farmakis, Ioannis Verfasser (DE-588)1043300783 aut Fixed point theorems and their applications Ioannis Farmakis ; Martin Moskowitz New Jersey [u.a.] World Scientific 2013 XI, 234 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Fixpunkttheorie (DE-588)4293945-8 gnd rswk-swf Fixpunkttheorie (DE-588)4293945-8 s DE-604 Moskowitz, Martin A. Verfasser (DE-588)114556628 aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026129545&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026129545&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Farmakis, Ioannis Moskowitz, Martin A. Fixed point theorems and their applications Fixpunkttheorie (DE-588)4293945-8 gnd |
| subject_GND | (DE-588)4293945-8 |
| title | Fixed point theorems and their applications |
| title_auth | Fixed point theorems and their applications |
| title_exact_search | Fixed point theorems and their applications |
| title_full | Fixed point theorems and their applications Ioannis Farmakis ; Martin Moskowitz |
| title_fullStr | Fixed point theorems and their applications Ioannis Farmakis ; Martin Moskowitz |
| title_full_unstemmed | Fixed point theorems and their applications Ioannis Farmakis ; Martin Moskowitz |
| title_short | Fixed point theorems and their applications |
| title_sort | fixed point theorems and their applications |
| topic | Fixpunkttheorie (DE-588)4293945-8 gnd |
| topic_facet | Fixpunkttheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026129545&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026129545&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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