Heights of polynomials and entropy in algebraic dynamics:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
London [u.a.]
Springer
1999
|
| Schriftenreihe: | Universitext
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008462114&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturverz. S. 199 - 207 |
| Umfang: | XII, 211 S. graph. Darst. |
| ISBN: | 1852331259 |
Internformat
MARC
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| 245 | 1 | 0 | |a Heights of polynomials and entropy in algebraic dynamics |c Graham Everest ; Thomas Ward |
| 264 | 1 | |a London [u.a.] |b Springer |c 1999 | |
| 300 | |a XII, 211 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Universitext | |
| 500 | |a Literaturverz. S. 199 - 207 | ||
| 650 | 7 | |a Dynamische systemen |2 gtt | |
| 650 | 7 | |a Ergodiciteit |2 gtt | |
| 650 | 7 | |a Geometria analitica |2 larpcal | |
| 650 | 7 | |a Krommen |2 gtt | |
| 650 | 4 | |a Arithmetical algebraic geometry | |
| 650 | 4 | |a Curves, Elliptic | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Measure theory | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008462114 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 144f 2001 A 13520 |
|---|---|
| DE-BY-TUM_katkey | 1144370 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010676754 |
| _version_ | 1821932320885571584 |
| adam_text | Contents
1. Lehmer, Mahler and Jensen 1
1.1 Background: Lehmer s Paper 1
1.2 Mahler s Measure 3
1.3 Lehmer s Problem I: Schinzel s Theorem 13
1.4 Lehmer s Problem II: Smyth s Theorem 15
1.5 Lehmer s Problem III: Zhang s Theorem 21
1.6 Large Primes in 1933 25
1.7 When Does the Measure Vanish? 27
2. Dynamical Systems 29
2.1 Dynamical Interpretation: Toral Case 29
2.2 Topological Entropy 34
2.3 Dynamical Interpretation: Solenoid Case 39
2.4 Periodic Points in the Dynamical Interpretation 48
3. Mahler s Measure in Many Variables 51
3.1 Explicit Values 52
3.2 Existence 57
3.3 When Does the Measure Vanish? 59
3.4 Approximations to Two Dimensional Mahler Measure 69
3.5 Lawton s Estimate 73
3.6 Boyd s Example 79
4. Higher Dimensional Dynamical Systems 81
4.1 The Dynamical System Associated to a Polynomial 81
4.2 Mahler Measures as Entropies 82
4.3 Periodic Point Behaviour 86
4.4 Dynamical Zeta Functions 89
5. Elliptic Heights 91
5.1 Elliptic Curves 91
5.2 Explicit Formulae 95
5.3 Torsion Points of Order 11 99
5.4 Rational Points 100
xii Contents
5.5 Heights on Elliptic Curves 101
5.6 Mordell s Theorem 106
5.7 The Parallelogram Law and the Canonical Height 109
5.8 Heights of Algebraic Numbers 114
6. The Elliptic Mahler Measure 117
6.1 Elliptic Functions 117
6.2 Elliptic Mahler 124
6.3 Elliptic Mahler in Several Variables 131
6.4 Elliptic Mahler and Periodic Points 137
6.5 Application to the Division Polynomial 140
6.6 Elliptic Mahler and Dynamical Systems 142
A. Algebra 145
A.I Algebraic Integers 145
A.2 Integer Matrices 147
A.3 Hilbert s Nullstellensatz 148
B. Analysis 151
B.I Stone Weierstrass Theorem 151
B.2 The Gelfand Transform 154
C. Division Polynomials 157
D. Proof of Mahler s Bound for m(F ) 159
E. Calculations on An{F) and En(F) 165
E. 1 Lehmer Primes 165
E.2 Elliptic Primes 166
F. Exercises and Questions 169
F.I Hints for the Exercises 169
F.2 List of Questions 194
G. List of Notation 197
Bibliography 199
Index 209
|
| any_adam_object | 1 |
| author | Everest, Graham 1957-2010 Ward, Thomas |
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| classification_tum | MAT 390f |
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| dewey-full | 516.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/5 |
| dewey-search | 516.3/5 |
| dewey-sort | 3516.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012468686 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:30:50Z |
| institution | BVB |
| isbn | 1852331259 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008462114 |
| oclc_num | 40298416 |
| open_access_boolean | |
| owner | DE-824 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-634 |
| owner_facet | DE-824 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-634 |
| physical | XII, 211 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spellingShingle | Everest, Graham 1957-2010 Ward, Thomas Heights of polynomials and entropy in algebraic dynamics Dynamische systemen gtt Ergodiciteit gtt Geometria analitica larpcal Krommen gtt Arithmetical algebraic geometry Curves, Elliptic Differentiable dynamical systems Measure theory Dynamisches System (DE-588)4013396-5 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Arithmetische Geometrie (DE-588)4131383-5 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4001161-6 (DE-588)4131383-5 |
| title | Heights of polynomials and entropy in algebraic dynamics |
| title_auth | Heights of polynomials and entropy in algebraic dynamics |
| title_exact_search | Heights of polynomials and entropy in algebraic dynamics |
| title_full | Heights of polynomials and entropy in algebraic dynamics Graham Everest ; Thomas Ward |
| title_fullStr | Heights of polynomials and entropy in algebraic dynamics Graham Everest ; Thomas Ward |
| title_full_unstemmed | Heights of polynomials and entropy in algebraic dynamics Graham Everest ; Thomas Ward |
| title_short | Heights of polynomials and entropy in algebraic dynamics |
| title_sort | heights of polynomials and entropy in algebraic dynamics |
| topic | Dynamische systemen gtt Ergodiciteit gtt Geometria analitica larpcal Krommen gtt Arithmetical algebraic geometry Curves, Elliptic Differentiable dynamical systems Measure theory Dynamisches System (DE-588)4013396-5 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Arithmetische Geometrie (DE-588)4131383-5 gnd |
| topic_facet | Dynamische systemen Ergodiciteit Geometria analitica Krommen Arithmetical algebraic geometry Curves, Elliptic Differentiable dynamical systems Measure theory Dynamisches System Algebraische Geometrie Arithmetische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008462114&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT everestgraham heightsofpolynomialsandentropyinalgebraicdynamics AT wardthomas heightsofpolynomialsandentropyinalgebraicdynamics |
Inhaltsverzeichnis
Paper/Kapitel scannen lassen
Paper/Kapitel scannen lassen
Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 144f 2001 A 13520 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |