Isochronous systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Oxford Univ. Press
2008
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 250 S. |
| ISBN: | 9780199535286 9780199657520 |
Internformat
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| 100 | 1 | |a Calogero, Francesco |d 1935- |e Verfasser |0 (DE-588)112739245 |4 aut | |
| 245 | 1 | 0 | |a Isochronous systems |c Francesco Calogero |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a New York [u.a.] |b Oxford Univ. Press |c 2008 | |
| 300 | |a X, 250 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Analyse de systèmes | |
| 650 | 4 | |a Dynamique | |
| 650 | 4 | |a Équations différentielles | |
| 650 | 4 | |a Dynamics | |
| 650 | 4 | |a System analysis | |
| 650 | 4 | |a Differential equations | |
| 650 | 0 | 7 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016492064 | ||
Datensatz im Suchindex
| _version_ | 1804137639970865152 |
|---|---|
| adam_text | CONTENTS
1
Introduction
χ
l.N Notes to Chapter
1 7
2
Isochronous systems are not rare
9
2.1
The trick
9
2.2
Examples
13
2.N Notes to Chapter
2 21
3
A single ODE of arbitrary order
23
3.1
A class of autonomous ODEs
23
3.2
Examples
31
3.2.1
First-order algebraic complex ODE
32
3.2.2
Polynomial vector field in the plane
33
3.2.3
Oscillator with additional inverse-cube force
34
3.2.4
Isochronous versions of the first and second
Painlevć
ODEs (complex and real versions)
34
3.2.5
Autonomous second-order ODEs (complex and real
versions)
35
3.2.6
Autonomous third-order ODEs (complex and real
versions)
42
3.2.7
Isochronous version of a solvable second-order ODE
due to
Painlevé
44
3.2.8
Isochronous versions of five solvable ODEs due to
Chazy
46
3.N Notes to Chapter
3 50
4
Systems of ODEs: many-body problems, nonlinear
harmonic oscillators
51
4.1
A class of isochronous dynamical systems
52
4.1.1
A lemma
53
4.1.2
Examples
60
4.2
One-dimensional systems
69
4.2.1
Many-body problems with two-body velocity-independent
forces
69
4.2.2
Goldfishing
69
4.2.3
Nonlinear oscillators
114
4.2.4
Two Hamiltoniau systems
115
4.3
Two-dimensional systems
120
4.4
Three-dimensional svstems
123
χ
Contents
4.5
Multi-dimensional systems
127
4.N Notes to Chapter
4 131
5
Isochronous Hamiltonian systems are not rare
135
5.1
Another trick
136
5.2
Partially isochronous Hamiltonian systems
148
5.2.1
A simple variant
149
5.2.2
A more general variant
151
5.3
More general Hamiltonians
153
5.4
Examples
155
5.5
Yet another trick
163
5.5.1
Main results
164
5.5.2
Transient chaos
169
5.5.3
A simple example
170
5.5.4
Quantization: equispaced spectrum
172
5.N Notes to Chapter
5 174
6
Asymptotically isochronous systems
176
6.1
An asymptotically isochronous class of solvable
many-body problems
177
6.1.1
A specific example
179
6.2
A (generally nonintegrable) class of asymptotically
isochronous many-body models
180
6.2.1
A theorem and its proof
182
6.3
Some additional considerations
185
7
Isochronous PDEs
188
7.1
The trick for PDEs
188
7.2
A list of isochronous PDEs
190
7.3
PDEs with lots of solutions periodic in time and in space
206
7.N Notes to Chapter
7 208
8
Outlook
211
8.N Notes to Chapter
8 212
A Some useful identities
213
В
Two proofs
218
С
Diophantine findings and conjectures
229
References
239
Index
249
|
| adam_txt |
CONTENTS
1
Introduction
χ
l.N Notes to Chapter
1 7
2
Isochronous systems are not rare
9
2.1
The trick
9
2.2
Examples
13
2.N Notes to Chapter
2 21
3
A single ODE of arbitrary order
23
3.1
A class of autonomous ODEs
23
3.2
Examples
31
3.2.1
First-order algebraic complex ODE
32
3.2.2
Polynomial vector field in the plane
33
3.2.3
Oscillator with additional inverse-cube force
34
3.2.4
Isochronous versions of the first and second
Painlevć
ODEs (complex and real versions)
34
3.2.5
Autonomous second-order ODEs (complex and real
versions)
35
3.2.6
Autonomous third-order ODEs (complex and real
versions)
42
3.2.7
Isochronous version of a solvable second-order ODE
due to
Painlevé
44
3.2.8
Isochronous versions of five solvable ODEs due to
Chazy
46
3.N Notes to Chapter
3 50
4
Systems of ODEs: many-body problems, nonlinear
harmonic oscillators
51
4.1
A class of isochronous dynamical systems
52
4.1.1
A lemma
53
4.1.2
Examples
60
4.2
One-dimensional systems
69
4.2.1
Many-body problems with two-body velocity-independent
forces
69
4.2.2
Goldfishing
69
4.2.3
Nonlinear oscillators
114
4.2.4
Two Hamiltoniau systems
115
4.3
Two-dimensional systems
120
4.4
Three-dimensional svstems
123
χ
Contents
4.5
Multi-dimensional systems
127
4.N Notes to Chapter
4 131
5
Isochronous Hamiltonian systems are not rare
135
5.1
Another trick
136
5.2
Partially isochronous Hamiltonian systems
148
5.2.1
A simple variant
149
5.2.2
A more general variant
151
5.3
More general Hamiltonians
153
5.4
Examples
155
5.5
Yet another trick
163
5.5.1
Main results
164
5.5.2
Transient chaos
169
5.5.3
A simple example
170
5.5.4
Quantization: equispaced spectrum
172
5.N Notes to Chapter
5 174
6
Asymptotically isochronous systems
176
6.1
An asymptotically isochronous class of solvable
many-body problems
177
6.1.1
A specific example
179
6.2
A (generally nonintegrable) class of asymptotically
isochronous many-body models
180
6.2.1
A theorem and its proof
182
6.3
Some additional considerations
185
7
Isochronous PDEs
188
7.1
The trick for PDEs
188
7.2
A list of isochronous PDEs
190
7.3
PDEs with lots of solutions periodic in time and in space
206
7.N Notes to Chapter
7 208
8
Outlook
211
8.N Notes to Chapter
8 212
A Some useful identities
213
В
Two proofs
218
С
Diophantine findings and conjectures
229
References
239
Index
249 |
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| author | Calogero, Francesco 1935- |
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T20:49:10Z |
| indexdate | 2024-07-09T21:15:30Z |
| institution | BVB |
| isbn | 9780199535286 9780199657520 |
| language | English |
| lccn | 2007047123 |
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| physical | X, 250 S. |
| publishDate | 2008 |
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| publisher | Oxford Univ. Press |
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| spelling | Calogero, Francesco 1935- Verfasser (DE-588)112739245 aut Isochronous systems Francesco Calogero 1. publ. New York [u.a.] Oxford Univ. Press 2008 X, 250 S. txt rdacontent n rdamedia nc rdacarrier Analyse de systèmes Dynamique Équations différentielles Dynamics System analysis Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016492064&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Calogero, Francesco 1935- Isochronous systems Analyse de systèmes Dynamique Équations différentielles Dynamics System analysis Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4020929-5 |
| title | Isochronous systems |
| title_auth | Isochronous systems |
| title_exact_search | Isochronous systems |
| title_exact_search_txtP | Isochronous systems |
| title_full | Isochronous systems Francesco Calogero |
| title_fullStr | Isochronous systems Francesco Calogero |
| title_full_unstemmed | Isochronous systems Francesco Calogero |
| title_short | Isochronous systems |
| title_sort | isochronous systems |
| topic | Analyse de systèmes Dynamique Équations différentielles Dynamics System analysis Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Analyse de systèmes Dynamique Équations différentielles Dynamics System analysis Differential equations Gewöhnliche Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016492064&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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