Lectures on analytic differential equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2008
|
| Schriftenreihe: | Graduate Studies in Mathematics
86 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 625 Seiten graph. Darst. |
| ISBN: | 9780821836675 |
Internformat
MARC
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| 100 | 1 | |a Ilʹjašenko, Julij S. |d 1943- |e Verfasser |0 (DE-588)134211898 |4 aut | |
| 245 | 1 | 0 | |a Lectures on analytic differential equations |c Yulij Ilyashenko, Sergei Yakovenko |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2008 | |
| 300 | |a XIII, 625 Seiten |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate Studies in Mathematics |v 86 | |
| 650 | 4 | |a Differentialligninger | |
| 650 | 4 | |a Differential equations, Nonlinear | |
| 650 | 4 | |a Riemann-Hilbert problems | |
| 650 | 4 | |a Analytics spaces | |
| 650 | 4 | |a Dynamics | |
| 650 | 0 | 7 | |a Analytischer Raum |0 (DE-588)4001871-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Riemann-Hilbert-Problem |0 (DE-588)4372594-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Analytische Differentialgleichung |0 (DE-588)4629102-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Holomorphie |0 (DE-588)4160484-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Analytische Differentialgleichung |0 (DE-588)4629102-7 |D s |
| 689 | 0 | 1 | |a Riemann-Hilbert-Problem |0 (DE-588)4372594-6 |D s |
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| 689 | 0 | 3 | |a Holomorphie |0 (DE-588)4160484-2 |D s |
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| 700 | 1 | |a Yakovenko, Sergei |d 1960- |e Verfasser |0 (DE-588)134211715 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-2116-8 |
| 830 | 0 | |a Graduate Studies in Mathematics |v 86 |w (DE-604)BV009739289 |9 86 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016304407&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016304407 | ||
Datensatz im Suchindex
| _version_ | 1804137360080764928 |
|---|---|
| adam_text | Contents
Preface
ix
Chapter I. Normal forms and desingularization
1
1.
Analytic differential equations in the complex domain
1
2.
Holomorphic foliations and their singularities
13
3.
Formal flows and embedding theorem
29
4.
Formal normal forms
40
5.
Holomorphic normal forms
61
6.
Finitely generated groups of
conformai
germs
81
7.
Holomorphic invariant manifolds
105
8.
Desingularization in the plane
112
Chapter II. Singular points of planar analytic vector fields
143
9.
Planar vector fields with characteristic trajectories
143
10.
Algebraic decidability of local problems and center-focus
alternative
159
11.
Holonomy and first integrals
179
12.
Zeros of parametric families of analytic functions
and small amplitude limit cycles
200
13.
Quadratic vector fields and the Bautin theorem
223
14.
Complex
séparatrices
of holomorphic foliations
232
Chapter III. Local and global theory of linear systems
255
15.
General facts about linear systems
255
16.
Local theory of regular singular points and applications
265
vii
viii Contents
17.
Global
theory of linear systems: holomorphic vector bundles
and meromorphic connexions
285
18.
Riemann-Hilbert problem
312
19.
Linear nth order differential equations
329
20.
Irregular singularities and the Stokes phenomenon
351
Appendix: Demonstration of Sibuya theorem
365
Chapter IV. Functional moduli of analytic classification of resonant
germs and their applications
373
21.
Nonlinear Stokes phenomenon for parabolic and resonant germs
of holomorphic self-maps
373
22.
Complex saddles and saddle-nodes
404
23.
Nonlinear Riemann-Hilbert problem
428
24.
Nonaccumulation theorem for hyperbolic polycycles
442
Chapter V. Global properties of complex polynomial foliations
469
25.
Algebraic leaves of polynomial foliations on the complex
projective
plane P2
470
Appendix: Foliations with invariant lines and algebraic leaves of
foliations from the class Ar
499
26.
Perturbations of Hamiltonian vector fields and zeros of Abelian
integrals
505
27.
Topological classification of complex linear foliations
545
28.
Global properties of generic polynomial foliations of the complex
projective
plane P2
567
First aid
599
A. Crash course on functions of several complex variables
599
B. Elements of the theory of Riemann surfaces.
603
Bibliography
607
Index
621
|
| adam_txt |
Contents
Preface
ix
Chapter I. Normal forms and desingularization
1
1.
Analytic differential equations in the complex domain
1
2.
Holomorphic foliations and their singularities
13
3.
Formal flows and embedding theorem
29
4.
Formal normal forms
40
5.
Holomorphic normal forms
61
6.
Finitely generated groups of
conformai
germs
81
7.
Holomorphic invariant manifolds
105
8.
Desingularization in the plane
112
Chapter II. Singular points of planar analytic vector fields
143
9.
Planar vector fields with characteristic trajectories
143
10.
Algebraic decidability of local problems and center-focus
alternative
159
11.
Holonomy and first integrals
179
12.
Zeros of parametric families of analytic functions
and small amplitude limit cycles
200
13.
Quadratic vector fields and the Bautin theorem
223
14.
Complex
séparatrices
of holomorphic foliations
232
Chapter III. Local and global theory of linear systems
255
15.
General facts about linear systems
255
16.
Local theory of regular singular points and applications
265
vii
viii Contents
17.
Global
theory of linear systems: holomorphic vector bundles
and meromorphic connexions
285
18.
Riemann-Hilbert problem
312
19.
Linear nth order differential equations
329
20.
Irregular singularities and the Stokes phenomenon
351
Appendix: Demonstration of Sibuya theorem
365
Chapter IV. Functional moduli of analytic classification of resonant
germs and their applications
373
21.
Nonlinear Stokes phenomenon for parabolic and resonant germs
of holomorphic self-maps
373
22.
Complex saddles and saddle-nodes
404
23.
Nonlinear Riemann-Hilbert problem
428
24.
Nonaccumulation theorem for hyperbolic polycycles
442
Chapter V. Global properties of complex polynomial foliations
469
25.
Algebraic leaves of polynomial foliations on the complex
projective
plane P2
470
Appendix: Foliations with invariant lines and algebraic leaves of
foliations from the class Ar
499
26.
Perturbations of Hamiltonian vector fields and zeros of Abelian
integrals
505
27.
Topological classification of complex linear foliations
545
28.
Global properties of generic polynomial foliations of the complex
projective
plane P2
567
First aid
599
A. Crash course on functions of several complex variables
599
B. Elements of the theory of Riemann surfaces.
603
Bibliography
607
Index
621 |
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| ctrlnum | (OCoLC)474186621 (DE-599)DNB 2007060785 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
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| id | DE-604.BV023101691 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:44:55Z |
| indexdate | 2024-07-09T21:11:03Z |
| institution | BVB |
| isbn | 9780821836675 |
| language | English |
| lccn | 2007060785 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016304407 |
| oclc_num | 474186621 |
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| physical | XIII, 625 Seiten graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Graduate Studies in Mathematics |
| series2 | Graduate Studies in Mathematics |
| spelling | Ilʹjašenko, Julij S. 1943- Verfasser (DE-588)134211898 aut Lectures on analytic differential equations Yulij Ilyashenko, Sergei Yakovenko Providence, RI American Mathematical Society 2008 XIII, 625 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate Studies in Mathematics 86 Differentialligninger Differential equations, Nonlinear Riemann-Hilbert problems Analytics spaces Dynamics Analytischer Raum (DE-588)4001871-4 gnd rswk-swf Riemann-Hilbert-Problem (DE-588)4372594-6 gnd rswk-swf Analytische Differentialgleichung (DE-588)4629102-7 gnd rswk-swf Holomorphie (DE-588)4160484-2 gnd rswk-swf Analytische Differentialgleichung (DE-588)4629102-7 s Riemann-Hilbert-Problem (DE-588)4372594-6 s Analytischer Raum (DE-588)4001871-4 s Holomorphie (DE-588)4160484-2 s DE-604 Yakovenko, Sergei 1960- Verfasser (DE-588)134211715 aut Erscheint auch als Online-Ausgabe 978-1-4704-2116-8 Graduate Studies in Mathematics 86 (DE-604)BV009739289 86 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016304407&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ilʹjašenko, Julij S. 1943- Yakovenko, Sergei 1960- Lectures on analytic differential equations Graduate Studies in Mathematics Differentialligninger Differential equations, Nonlinear Riemann-Hilbert problems Analytics spaces Dynamics Analytischer Raum (DE-588)4001871-4 gnd Riemann-Hilbert-Problem (DE-588)4372594-6 gnd Analytische Differentialgleichung (DE-588)4629102-7 gnd Holomorphie (DE-588)4160484-2 gnd |
| subject_GND | (DE-588)4001871-4 (DE-588)4372594-6 (DE-588)4629102-7 (DE-588)4160484-2 |
| title | Lectures on analytic differential equations |
| title_auth | Lectures on analytic differential equations |
| title_exact_search | Lectures on analytic differential equations |
| title_exact_search_txtP | Lectures on analytic differential equations |
| title_full | Lectures on analytic differential equations Yulij Ilyashenko, Sergei Yakovenko |
| title_fullStr | Lectures on analytic differential equations Yulij Ilyashenko, Sergei Yakovenko |
| title_full_unstemmed | Lectures on analytic differential equations Yulij Ilyashenko, Sergei Yakovenko |
| title_short | Lectures on analytic differential equations |
| title_sort | lectures on analytic differential equations |
| topic | Differentialligninger Differential equations, Nonlinear Riemann-Hilbert problems Analytics spaces Dynamics Analytischer Raum (DE-588)4001871-4 gnd Riemann-Hilbert-Problem (DE-588)4372594-6 gnd Analytische Differentialgleichung (DE-588)4629102-7 gnd Holomorphie (DE-588)4160484-2 gnd |
| topic_facet | Differentialligninger Differential equations, Nonlinear Riemann-Hilbert problems Analytics spaces Dynamics Analytischer Raum Riemann-Hilbert-Problem Analytische Differentialgleichung Holomorphie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016304407&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009739289 |
| work_keys_str_mv | AT ilʹjasenkojulijs lecturesonanalyticdifferentialequations AT yakovenkosergei lecturesonanalyticdifferentialequations |