Integrability of dynamical systems: algebra and analysis
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore
Springer
[2017]
|
| Ausgabe: | [1st edition] |
| Schriftenreihe: | Developments in mathematics
volume 47 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext http://www.springer.com/ Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | xv, 380 Seiten 24 cm |
| ISBN: | 9789811042256 981104225X |
Internformat
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| 245 | 1 | 0 | |a Integrability of dynamical systems |b algebra and analysis |c Xiang Zhang |
| 250 | |a [1st edition] | ||
| 264 | 1 | |a Singapore |b Springer |c [2017] | |
| 264 | 4 | |c @ 2017 | |
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| 653 | |a integrability | ||
| 653 | |a Jacobian multipliers | ||
| 653 | |a Darboux integrability | ||
| 653 | |a Liouvillian integrability | ||
| 653 | |a Darboux polynomials | ||
| 653 | |a Local integrability | ||
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Datensatz im Suchindex
| _version_ | 1804181802210820096 |
|---|---|
| adam_text | CONTENTS
1 THE FUNDAMENTALS OF THE THEORY OF INTEGRABILITY
OF DIFFERENTIAL SYSTEMS. 1
1.1 EXISTENCE AND PROPERTIES OF THE FIRST INTEGRALS. 1
1.1.1 CHARACTERIZATION AND PROPERTIES OF THE FIRST INTEGRALS. 3
1.1.2 EXISTENCE OF FIRST INTEGRALS NEAR A REGULAR POINT. 7
1.2 FIRST INTEGRALS OF DIFFERENTIAL SYSTEMS IN CANONICAL REGIONS. 10
1.3 APPLICATIONS OF INTEGRABILITY THEORY TO PARTIAL DIFFERENTIAL
EQUATIONS. 20
1.3.1 FIRST-ORDER LINEAR HOMOGENEOUS PARTIAL DIFFERENTIAL
EQUATIONS. 21
1.3.2 FIRST-ORDER QUASILINEAR PARTIAL DIFFERENTIAL EQUATIONS. 23
1.4 LAX PAIRS AND INTEGRABILITY. 26
2 JACOBIAN AND INVERSE JACOBIAN MULTIPLIERS. 35
2.1 JACOBIAN MULTIPLIERS, FIRST INTEGRALS AND INTEGRABILITY.*. 35
2.2 INVERSE JACOBIAN MULTIPLIERS AND THEIR VANISHING SETS. 45
2.3 INVERSE JACOBIAN MULTIPLIERS AND THE CENTER-FOCUS PROBLEM. 59
2.3.1 THE CENTER-FOCUS PROBLEM VIA INVERSE INTEGRATING
FACTORS OR INVERSE JACOBIAN MULTIPLIERS. 61
2.3.2 HOPF BIFURCATION VIA INVERSE JACOBIAN MULTIPLIERS. 73
2.4 INVERSE JACOBIAN MULTIPLIERS VIA LIE GROUPS. 79
3 DARBOUX AND LIOUVILLIAN INTEGRABILITY. 89
3.1 THE CLASSICAL DARBOUX THEORY OF INTEGRABILITY. 89
3.1.1 THE EXISTENCE OF DARBOUX FIRST INTEGRALS. 90
3.1.2 THE DARBOUX-JOUANOLOU INTEGRABILITY THEOREM. 94
3.2 GENERALIZATION OF THE CLASSICAL DARBOUX THEORY
OF INTEGRABILITY. 98
3.2.1 TAKING INTO ACCOUNT INDEPENDENT SINGULARITIES. 98
3.2.2 TAKING INTO ACCOUNT ALGEBRAIC MULTIPLICITIES. 100
IX
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/1125641622
X
CONTENTS
3.2.3 TAKING INTO ACCOUNT THE MULTIPLICITY OF THE HYPERPLANE
AT INFINITY. 113
3.2.4 ON NONAUTONOMOUS DIFFERENTIAL SYSTEMS
VIA THE WRONSKIAN MATRIX. 115
3.2.5 DIFFERENTIAL SYSTEMS IN THE SPARSE CASE. 122
3.2.6 OTHER EXTENSIONS. 125
3.3 LIOUVILLE AND ELEMENTARY FIRST INTEGRALS... 126
3.3.1 BACKGROUND ON DIFFERENTIAL FIELD EXTENSIONS. 126
3.3.2 THE PRELIE AND SINGER INTEGRABILITY THEOREMS. 131
3.4 LIOUVILLIAN INTEGRABILITY VERSUS DARBOUX POLYNOMIALS. 145
4 EXISTENCE AND DEGREE OF DARBOUX POLYNOMIALS. 149
4.1 THE DEGREE OF INVARIANT ALGEBRAIC CURVES. 149
4.1.1 EXAMPLES OF INVARIANT ALGEBRAIC CURVES
OF ARBITRARY DEGREE. 150
4.1.2 INVARIANT ALGEBRAIC CURVES IN THE PROJECTIVE PLANE. 152
4.1.3 THE DEGREE OF INVARIANT ALGEBRAIC CURVES
IN THE NODAL AND NONDICRITICAL CASES. 156
4.2 EXISTENCE OF DARBOUX POLYNOMIALS. 163
4.2.1 POLYNOMIAL VECTOR FIELDS WITHOUT DARBOUX
POLYNOMIALS. 164
4.2.2 LIENARD DIFFERENTIAL SYSTEMS: INVARIANT ALGEBRAIC
CURVES. 167
4.2.3 LORENZ SYSTEMS: INVARIANT ALGEBRAIC SURFACES. 177
4.3 OTHER RESULTS ON DARBOUX POLYNOMIALS. 192
5 ALGEBRAIC, ANALYTIC AND MEROMORPHIC INTEGRABILITY. 197
5.1 ALGEBRAIC FIRST INTEGRALS. 197
5.1.1 ALGEBRAIC AND RATIONAL INTEGRABILITY: THEIR
EQUIVALENCE. 197
5.1.2 KIRCHOFIF EQUATIONS: POLYNOMIAL AND RATIONAL FIRST
INTEGRALS. 200
5.1.3 EULER EQUATIONS ON THE LIE ALGEBRA SO(4): POLYNOMIAL
FIRST INTEGRALS. 211
5.1.4 THE 5-DIMENSIONAL LORENZ SYSTEMS: DARBOUX AND
ANALYTIC INTEGRABILITY. 216
5.2 NATURAL HAMILTONIAN SYSTEMS: POLYNOMIAL AND RATIONAL
INTEGRABILITY. 221
5.2.1 HAMILTONIAN SYSTEMS IN THE CANONICAL FORM. 221
5.2.2 HAMILTONIAN SYSTEMS IN A GENERALIZED FORM. 225
5.3 HAMILTONIAN SYSTEMS: INTEGRABILITY VIA THE DIFFERENTIAL GALOIS
GROUP. 227
5.3.1 HAMILTONIAN SYSTEMS HAVING HOMOGENEOUS POTENTIALS.. .. 228
5.3.2 HAMILTONIAN SYSTEMS: INTEGRABILITY VIA OTHER
EXTENSIONS. 236
CONTENTS
XI
5.3.3 EXTENSION OF THE MORALES-RAMIS THEORY TO GENERAL
SYSTEMS. 239
5.4 CALCULATIONS OF RATIONAL FIRST INTEGRALS AND DARBOUX
POLYNOMIALS OF PLANAR POLYNOMIAL VECTOR FIELDS. 240
6 APPLICATIONS OF THE DARBOUX THEORY OF INTEGRABILITY. 253
6.1 THE CENTER PROBLEM VIA THE DARBOUX THEORY OF INTEGRABILITY. 253
6.2 ALGEBRAIC LIMIT CYCLES: EXISTENCE AND UNIQUENESS. 258
6.2.1 THE EXISTENCE OF RATIONAL FIRST INTEGRALS
VIA INTERSECTION NUMBERS. 259
6.2.2 QUADRATIC DIFFERENTIAL SYSTEMS: ALGEBRAIC
LIMIT CYCLES. 265
6.3 HILBERT S 16TH PROBLEM: A WEAK VERSION ON ALGEBRAIC
LIMIT CYCLES. 269
6.4 APPLICATIONS TO CONCRETE MODELS. 276
6.4.1 CONCRETE TWO-DIMENSIONAL MODELS IN APPLICATIONS. 276
6.4.2 CONCRETE THREE-DIMENSIONAL MODELS IN APPLICATIONS. 277
6.4.3 CONCRETE HIGHER-DIMENSIONAL MODELS IN APPLICATIONS .... 282
6.4.4 ABEL EQUATIONS AND FOLIATIONS. 283
7 LOCAL INTEGRABILITY OF DIFFERENTIAL SYSTEMS. 287
7.1 THE FOUNDATIONS OF POINCARE NORMAL FORM THEORY. 289
7.2 LOCAL ANALYTIC AND FORMAL FIRST INTEGRALS. 295
7.2.1 LOCAL INTEGRABILITY VIA PARTIAL NONRESONANCES. 296
7.2.2 LOCAL INTEGRABILITY VIA RESONANCES.. 301
7.3 LOCAL (FORMAL) MEROMORPHIC FIRST INTEGRALS. 307
7.3.1 THE EQUIVALENCE BETWEEN ALGEBRAIC AND FUNCTIONAL
INDEPENDENCE. 308
7.3.2 THE LOWEST ORDER PARTS OF FUNCTIONALLY INDEPENDENT
FIRST INTEGRALS. 309
7.3.3 PROOF OF THE RESULTS ON FUNCTIONALLY INDEPENDENT
FIRST INTEGRALS..* * * * 312
7.4 THE LOCAL THEORY OF DARBOUX INTEGRABILITY. 314
7.4.1 LOCAL DARBOUX FIRST INTEGRALS. 315
7.4.2 APPLICATIONS OF THE LOCAL THEORY OF DARBOUX
INTEGRABILITY. 318
7.5 ANALYTIC NORMALIZATION OF ANALYTIC INTEGRABLE SYSTEMS. 320
7.5.1 EQUIVALENT CHARACTERIZATION OF ANALYTIC INTEGRABLE
SYSTEMS. 320
7.5.2 INTEGRABLE DISCRETE DYNAMICAL SYSTEMS
AND EMBEDDING FLOWS. 329
7.6 VARIETIES AND NORMALIZATION OF PARTIALLY INTEGRABLE SYSTEMS. 334
7.6.1 VARIETIES OF PARTIALLY INTEGRABLE SYSTEMS. 334
7.6.2 ANALYTIC NORMALIZATION OF PARTIALLY INTEGRABLE SYSTEMS.... 341
XII CONTENTS
7.6.3 GENERIC DIVERGENCE OF NORMALIZATIONS OF PARTIALLY
INTEGRABLE SYSTEMS. 343
7.7 OTHER RESULTS ON LOCAL INTEGRABILITY. 347
REFERENCES. 353
INDEX. 373
|
| adam_txt |
CONTENTS
1 THE FUNDAMENTALS OF THE THEORY OF INTEGRABILITY
OF DIFFERENTIAL SYSTEMS. 1
1.1 EXISTENCE AND PROPERTIES OF THE FIRST INTEGRALS. 1
1.1.1 CHARACTERIZATION AND PROPERTIES OF THE FIRST INTEGRALS. 3
1.1.2 EXISTENCE OF FIRST INTEGRALS NEAR A REGULAR POINT. 7
1.2 FIRST INTEGRALS OF DIFFERENTIAL SYSTEMS IN CANONICAL REGIONS. 10
1.3 APPLICATIONS OF INTEGRABILITY THEORY TO PARTIAL DIFFERENTIAL
EQUATIONS. 20
1.3.1 FIRST-ORDER LINEAR HOMOGENEOUS PARTIAL DIFFERENTIAL
EQUATIONS. 21
1.3.2 FIRST-ORDER QUASILINEAR PARTIAL DIFFERENTIAL EQUATIONS. 23
1.4 LAX PAIRS AND INTEGRABILITY. 26
2 JACOBIAN AND INVERSE JACOBIAN MULTIPLIERS. 35
2.1 JACOBIAN MULTIPLIERS, FIRST INTEGRALS AND INTEGRABILITY.*. 35
2.2 INVERSE JACOBIAN MULTIPLIERS AND THEIR VANISHING SETS. 45
2.3 INVERSE JACOBIAN MULTIPLIERS AND THE CENTER-FOCUS PROBLEM. 59
2.3.1 THE CENTER-FOCUS PROBLEM VIA INVERSE INTEGRATING
FACTORS OR INVERSE JACOBIAN MULTIPLIERS. 61
2.3.2 HOPF BIFURCATION VIA INVERSE JACOBIAN MULTIPLIERS. 73
2.4 INVERSE JACOBIAN MULTIPLIERS VIA LIE GROUPS. 79
3 DARBOUX AND LIOUVILLIAN INTEGRABILITY. 89
3.1 THE CLASSICAL DARBOUX THEORY OF INTEGRABILITY. 89
3.1.1 THE EXISTENCE OF DARBOUX FIRST INTEGRALS. 90
3.1.2 THE DARBOUX-JOUANOLOU INTEGRABILITY THEOREM. 94
3.2 GENERALIZATION OF THE CLASSICAL DARBOUX THEORY
OF INTEGRABILITY. 98
3.2.1 TAKING INTO ACCOUNT INDEPENDENT SINGULARITIES. 98
3.2.2 TAKING INTO ACCOUNT ALGEBRAIC MULTIPLICITIES. 100
IX
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/1125641622
X
CONTENTS
3.2.3 TAKING INTO ACCOUNT THE MULTIPLICITY OF THE HYPERPLANE
AT INFINITY. 113
3.2.4 ON NONAUTONOMOUS DIFFERENTIAL SYSTEMS
VIA THE WRONSKIAN MATRIX. 115
3.2.5 DIFFERENTIAL SYSTEMS IN THE SPARSE CASE. 122
3.2.6 OTHER EXTENSIONS. 125
3.3 LIOUVILLE AND ELEMENTARY FIRST INTEGRALS. 126
3.3.1 BACKGROUND ON DIFFERENTIAL FIELD EXTENSIONS. 126
3.3.2 THE PRELIE AND SINGER INTEGRABILITY THEOREMS. 131
3.4 LIOUVILLIAN INTEGRABILITY VERSUS DARBOUX POLYNOMIALS. 145
4 EXISTENCE AND DEGREE OF DARBOUX POLYNOMIALS. 149
4.1 THE DEGREE OF INVARIANT ALGEBRAIC CURVES. 149
4.1.1 EXAMPLES OF INVARIANT ALGEBRAIC CURVES
OF ARBITRARY DEGREE. 150
4.1.2 INVARIANT ALGEBRAIC CURVES IN THE PROJECTIVE PLANE. 152
4.1.3 THE DEGREE OF INVARIANT ALGEBRAIC CURVES
IN THE NODAL AND NONDICRITICAL CASES. 156
4.2 EXISTENCE OF DARBOUX POLYNOMIALS. 163
4.2.1 POLYNOMIAL VECTOR FIELDS WITHOUT DARBOUX
POLYNOMIALS. 164
4.2.2 LIENARD DIFFERENTIAL SYSTEMS: INVARIANT ALGEBRAIC
CURVES. 167
4.2.3 LORENZ SYSTEMS: INVARIANT ALGEBRAIC SURFACES. 177
4.3 OTHER RESULTS ON DARBOUX POLYNOMIALS. 192
5 ALGEBRAIC, ANALYTIC AND MEROMORPHIC INTEGRABILITY. 197
5.1 ALGEBRAIC FIRST INTEGRALS. 197
5.1.1 ALGEBRAIC AND RATIONAL INTEGRABILITY: THEIR
EQUIVALENCE. 197
5.1.2 KIRCHOFIF EQUATIONS: POLYNOMIAL AND RATIONAL FIRST
INTEGRALS. 200
5.1.3 EULER EQUATIONS ON THE LIE ALGEBRA SO(4): POLYNOMIAL
FIRST INTEGRALS. 211
5.1.4 THE 5-DIMENSIONAL LORENZ SYSTEMS: DARBOUX AND
ANALYTIC INTEGRABILITY. 216
5.2 NATURAL HAMILTONIAN SYSTEMS: POLYNOMIAL AND RATIONAL
INTEGRABILITY. 221
5.2.1 HAMILTONIAN SYSTEMS IN THE CANONICAL FORM. 221
5.2.2 HAMILTONIAN SYSTEMS IN A GENERALIZED FORM. 225
5.3 HAMILTONIAN SYSTEMS: INTEGRABILITY VIA THE DIFFERENTIAL GALOIS
GROUP. 227
5.3.1 HAMILTONIAN SYSTEMS HAVING HOMOGENEOUS POTENTIALS. . 228
5.3.2 HAMILTONIAN SYSTEMS: INTEGRABILITY VIA OTHER
EXTENSIONS. 236
CONTENTS
XI
5.3.3 EXTENSION OF THE MORALES-RAMIS THEORY TO GENERAL
SYSTEMS. 239
5.4 CALCULATIONS OF RATIONAL FIRST INTEGRALS AND DARBOUX
POLYNOMIALS OF PLANAR POLYNOMIAL VECTOR FIELDS. 240
6 APPLICATIONS OF THE DARBOUX THEORY OF INTEGRABILITY. 253
6.1 THE CENTER PROBLEM VIA THE DARBOUX THEORY OF INTEGRABILITY. 253
6.2 ALGEBRAIC LIMIT CYCLES: EXISTENCE AND UNIQUENESS. 258
6.2.1 THE EXISTENCE OF RATIONAL FIRST INTEGRALS
VIA INTERSECTION NUMBERS. 259
6.2.2 QUADRATIC DIFFERENTIAL SYSTEMS: ALGEBRAIC
LIMIT CYCLES. 265
6.3 HILBERT'S 16TH PROBLEM: A WEAK VERSION ON ALGEBRAIC
LIMIT CYCLES. 269
6.4 APPLICATIONS TO CONCRETE MODELS. 276
6.4.1 CONCRETE TWO-DIMENSIONAL MODELS IN APPLICATIONS. 276
6.4.2 CONCRETE THREE-DIMENSIONAL MODELS IN APPLICATIONS. 277
6.4.3 CONCRETE HIGHER-DIMENSIONAL MODELS IN APPLICATIONS . 282
6.4.4 ABEL EQUATIONS AND FOLIATIONS. 283
7 LOCAL INTEGRABILITY OF DIFFERENTIAL SYSTEMS. 287
7.1 THE FOUNDATIONS OF POINCARE NORMAL FORM THEORY. 289
7.2 LOCAL ANALYTIC AND FORMAL FIRST INTEGRALS. 295
7.2.1 LOCAL INTEGRABILITY VIA PARTIAL NONRESONANCES. 296
7.2.2 LOCAL INTEGRABILITY VIA RESONANCES. 301
7.3 LOCAL (FORMAL) MEROMORPHIC FIRST INTEGRALS. 307
7.3.1 THE EQUIVALENCE BETWEEN ALGEBRAIC AND FUNCTIONAL
INDEPENDENCE. 308
7.3.2 THE LOWEST ORDER PARTS OF FUNCTIONALLY INDEPENDENT
FIRST INTEGRALS. 309
7.3.3 PROOF OF THE RESULTS ON FUNCTIONALLY INDEPENDENT
FIRST INTEGRALS.* * * * 312
7.4 THE LOCAL THEORY OF DARBOUX INTEGRABILITY. 314
7.4.1 LOCAL DARBOUX FIRST INTEGRALS. 315
7.4.2 APPLICATIONS OF THE LOCAL THEORY OF DARBOUX
INTEGRABILITY. 318
7.5 ANALYTIC NORMALIZATION OF ANALYTIC INTEGRABLE SYSTEMS. 320
7.5.1 EQUIVALENT CHARACTERIZATION OF ANALYTIC INTEGRABLE
SYSTEMS. 320
7.5.2 INTEGRABLE DISCRETE DYNAMICAL SYSTEMS
AND EMBEDDING FLOWS. 329
7.6 VARIETIES AND NORMALIZATION OF PARTIALLY INTEGRABLE SYSTEMS. 334
7.6.1 VARIETIES OF PARTIALLY INTEGRABLE SYSTEMS. 334
7.6.2 ANALYTIC NORMALIZATION OF PARTIALLY INTEGRABLE SYSTEMS. 341
XII CONTENTS
7.6.3 GENERIC DIVERGENCE OF NORMALIZATIONS OF PARTIALLY
INTEGRABLE SYSTEMS. 343
7.7 OTHER RESULTS ON LOCAL INTEGRABILITY. 347
REFERENCES. 353
INDEX. 373 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Zhang, Xiang |
| author_GND | (DE-588)1136041230 |
| author_facet | Zhang, Xiang |
| author_role | aut |
| author_sort | Zhang, Xiang |
| author_variant | x z xz |
| building | Verbundindex |
| bvnumber | BV046917360 |
| classification_rvk | SK 520 |
| ctrlnum | (OCoLC)1188581803 (DE-599)DNB1125641622 |
| dewey-full | 515.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.352 |
| dewey-search | 515.352 |
| dewey-sort | 3515.352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | [1st edition] |
| format | Book |
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| id | DE-604.BV046917360 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T15:30:08Z |
| indexdate | 2024-07-10T08:57:26Z |
| institution | BVB |
| institution_GND | (DE-588)1065365012 |
| isbn | 9789811042256 981104225X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032326663 |
| oclc_num | 1188581803 |
| open_access_boolean | |
| owner | DE-83 |
| owner_facet | DE-83 |
| physical | xv, 380 Seiten 24 cm |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Springer |
| record_format | marc |
| series | Developments in mathematics |
| series2 | Developments in mathematics |
| spelling | Zhang, Xiang Verfasser (DE-588)1136041230 aut Integrability of dynamical systems algebra and analysis Xiang Zhang [1st edition] Singapore Springer [2017] @ 2017 xv, 380 Seiten 24 cm txt rdacontent n rdamedia nc rdacarrier Developments in mathematics volume 47 Integrierbarkeit (DE-588)4474751-2 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf integrability Jacobian multipliers Darboux integrability Liouvillian integrability Darboux polynomials Local integrability Dynamisches System (DE-588)4013396-5 s Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Integrierbarkeit (DE-588)4474751-2 s DE-604 Springer Malaysia Representative Office (DE-588)1065365012 pbl Erscheint auch als Online-Ausgabe Zhang, Xiang Integrability of Dynamical Systems: Algebra and Analysis 1st edition 2017 Singapore : Springer Singapore, 2017 Online-Ressourcen Developments in mathematics volume 47 (DE-604)BV013103064 47 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=80cd2c9a68f94fdbb96c6d565c35f504&prov=M&dok_var=1&dok_ext=htm Inhaltstext X:MVB http://www.springer.com/ B:DE-101 application/pdf https://d-nb.info/1125641622/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032326663&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zhang, Xiang Integrability of dynamical systems algebra and analysis Developments in mathematics Integrierbarkeit (DE-588)4474751-2 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4474751-2 (DE-588)4020929-5 (DE-588)4013396-5 |
| title | Integrability of dynamical systems algebra and analysis |
| title_auth | Integrability of dynamical systems algebra and analysis |
| title_exact_search | Integrability of dynamical systems algebra and analysis |
| title_exact_search_txtP | Integrability of dynamical systems algebra and analysis |
| title_full | Integrability of dynamical systems algebra and analysis Xiang Zhang |
| title_fullStr | Integrability of dynamical systems algebra and analysis Xiang Zhang |
| title_full_unstemmed | Integrability of dynamical systems algebra and analysis Xiang Zhang |
| title_short | Integrability of dynamical systems |
| title_sort | integrability of dynamical systems algebra and analysis |
| title_sub | algebra and analysis |
| topic | Integrierbarkeit (DE-588)4474751-2 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Integrierbarkeit Gewöhnliche Differentialgleichung Dynamisches System |
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| volume_link | (DE-604)BV013103064 |
| work_keys_str_mv | AT zhangxiang integrabilityofdynamicalsystemsalgebraandanalysis AT springermalaysiarepresentativeoffice integrabilityofdynamicalsystemsalgebraandanalysis |