The Resource Differential galois theory and non-integrability of hamiltonian systems, Juan J. Morales Ruiz

Differential galois theory and non-integrability of hamiltonian systems, Juan J. Morales Ruiz

Label
Differential galois theory and non-integrability of hamiltonian systems
Title
Differential galois theory and non-integrability of hamiltonian systems
Statement of responsibility
Juan J. Morales Ruiz
Creator
Author
Subject
Genre
Language
  • eng
  • eng
Summary
This book is devoted to the relation between two different concepts of integrability: the complete integrability of complex analytical Hamiltonian systems and the integrability of complex analytical linear differential equations. For linear differential equations, integrability is made precise within the framework of differential Galois theory. The connection of these two integrability notions is given by the variational equation (i.e. linearized equation) along a particular integral curve of the Hamiltonian system. The underlying heuristic idea, which motivated the main results presented in this monograph, is that a necessary condition for the integrability of a Hamiltonian system is the integrability of the variational equation along any of its particular integral curves. This idea led to the algebraic non-integrability criteria for Hamiltonian systems. These criteria can be considered as generalizations of classical non-integrability results by Poincaré and Lyapunov, as well as more recent results by Ziglin and Yoshida. Thus, by means of the differential Galois theory it is not only possible to understand all these approaches in a unified way but also to improve them. Several important applications are also included: homogeneous potentials, Bianchi IX cosmological model, three-body problem, Hénon-Heiles system, etc. The book is based on the original joint research of the author with J.M. Peris, J.P. Ramis and C. Simó, but an effort was made to present these achievements in their logical order rather than their historical one. The necessary background on differential Galois theory and Hamiltonian systems is included, and several new problems and conjectures which open new lines of research are proposed. - - - The book is an excellent introduction to non-integrability methods in Hamiltonian mechanics and brings the reader to the forefront of research in the area. The inclusion of a large number of worked-out examples, many of wide applied interest, is commendable. There are many historical references, and an extensive bibliography. (Mathematical Reviews) For readers already prepared in the two prerequisite subjects [differential Galois theory and Hamiltonian dynamical systems], the author has provided a logically accessible account of a remarkable interaction between differential algebra and dynamics. (Zentralblatt MATH)
Member of
Cataloging source
MiAaPQ
http://library.link/vocab/creatorName
Ruiz Morales, Juan J.
Dewey number
515.352
Image bit depth
0
Index
index present
Language note
English
LC call number
QC173.7
LC item number
.R859 1999
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Progress in Mathematics
Series volume
Volume 179
http://library.link/vocab/subjectName
  • Field theory (Physics)
  • Global analysis
  • Differential equations
Label
Differential galois theory and non-integrability of hamiltonian systems, Juan J. Morales Ruiz
Instantiates
Publication
Copyright
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
1 Introduction -- 2 Differential Galois Theory -- 2.1 Algebraic groups -- 2.2 Classical approach -- 2.3 Meromorphic connections -- 2.4 The Tannakian approach -- 2.5 Stokes multipliers -- 2.6 Coverings and differential Galois groups -- 2.7 Kovacic’s algorithm -- 2.8 Examples -- 3 Hamiltonian Systems -- 3.1 Definitions -- 3.2 Complete integrability -- 3.3 Three non-integrability theorems -- 3.4 Some properties of Poisson algebras -- 4 Non-integrability Theorems -- 4.1 Variational equations -- 4.2 Main results -- 4.3 Examples -- 5 Three Models -- 5.1 Homogeneous potentials -- 5.2 The Bianchi IX cosmological model -- 5.3 Sitnikov’s Three-Body Problem -- 6 An Application of the Lamé Equation -- 6.1 Computation of the potentials -- 6.2 Non-integrability criterion -- 6.3 Examples -- 6.4 The homogeneous Hénon-Heiles potential -- 7 A Connection with Chaotic Dynamics -- 7.1 Grotta-Ragazzo interpretation of Lerman’s theorem -- 7.2 Differential Galois approach -- 7.3 Example -- 8 Complementary Results and Conjectures -- 8.1 Two additional applications -- 8.2 A conjecture about the dynamic -- 8.3 Higher-order variational equations -- A Meromorphic Bundles -- B Galois Groups and Finite Coverings -- C Connections with Structure Group
Dimensions
unknown
Extent
1 online resource (XIV, 167 p. 5 illus.)
File format
multiple file formats
Form of item
online
Isbn
9783034887182
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-3-0348-8718-2
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000101689
  • (SSID)ssj0001296419
  • (PQKBManifestationID)11886452
  • (PQKBTitleCode)TC0001296419
  • (PQKBWorkID)11347979
  • (PQKB)10865808
  • (DE-He213)978-3-0348-8718-2
  • (MiAaPQ)EBC3087619
  • (EXLCZ)993400000000101689
Label
Differential galois theory and non-integrability of hamiltonian systems, Juan J. Morales Ruiz
Publication
Copyright
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
1 Introduction -- 2 Differential Galois Theory -- 2.1 Algebraic groups -- 2.2 Classical approach -- 2.3 Meromorphic connections -- 2.4 The Tannakian approach -- 2.5 Stokes multipliers -- 2.6 Coverings and differential Galois groups -- 2.7 Kovacic’s algorithm -- 2.8 Examples -- 3 Hamiltonian Systems -- 3.1 Definitions -- 3.2 Complete integrability -- 3.3 Three non-integrability theorems -- 3.4 Some properties of Poisson algebras -- 4 Non-integrability Theorems -- 4.1 Variational equations -- 4.2 Main results -- 4.3 Examples -- 5 Three Models -- 5.1 Homogeneous potentials -- 5.2 The Bianchi IX cosmological model -- 5.3 Sitnikov’s Three-Body Problem -- 6 An Application of the Lamé Equation -- 6.1 Computation of the potentials -- 6.2 Non-integrability criterion -- 6.3 Examples -- 6.4 The homogeneous Hénon-Heiles potential -- 7 A Connection with Chaotic Dynamics -- 7.1 Grotta-Ragazzo interpretation of Lerman’s theorem -- 7.2 Differential Galois approach -- 7.3 Example -- 8 Complementary Results and Conjectures -- 8.1 Two additional applications -- 8.2 A conjecture about the dynamic -- 8.3 Higher-order variational equations -- A Meromorphic Bundles -- B Galois Groups and Finite Coverings -- C Connections with Structure Group
Dimensions
unknown
Extent
1 online resource (XIV, 167 p. 5 illus.)
File format
multiple file formats
Form of item
online
Isbn
9783034887182
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-3-0348-8718-2
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000101689
  • (SSID)ssj0001296419
  • (PQKBManifestationID)11886452
  • (PQKBTitleCode)TC0001296419
  • (PQKBWorkID)11347979
  • (PQKB)10865808
  • (DE-He213)978-3-0348-8718-2
  • (MiAaPQ)EBC3087619
  • (EXLCZ)993400000000101689

Library Locations

  • Architecture LibraryBorrow it
    Gould Hall 830 Van Vleet Oval Rm. 105, Norman, OK, 73019, US
    35.205706 -97.445050
  • Bizzell Memorial LibraryBorrow it
    401 W. Brooks St., Norman, OK, 73019, US
    35.207487 -97.447906
  • Boorstin CollectionBorrow it
    401 W. Brooks St., Norman, OK, 73019, US
    35.207487 -97.447906
  • Chinese Literature Translation ArchiveBorrow it
    401 W. Brooks St., RM 414, Norman, OK, 73019, US
    35.207487 -97.447906
  • Engineering LibraryBorrow it
    Felgar Hall 865 Asp Avenue, Rm. 222, Norman, OK, 73019, US
    35.205706 -97.445050
  • Fine Arts LibraryBorrow it
    Catlett Music Center 500 West Boyd Street, Rm. 20, Norman, OK, 73019, US
    35.210371 -97.448244
  • Harry W. Bass Business History CollectionBorrow it
    401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US
    35.207487 -97.447906
  • History of Science CollectionsBorrow it
    401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US
    35.207487 -97.447906
  • John and Mary Nichols Rare Books and Special CollectionsBorrow it
    401 W. Brooks St., Rm. 509NW, Norman, OK, 73019, US
    35.207487 -97.447906
  • Library Service CenterBorrow it
    2601 Technology Place, Norman, OK, 73019, US
    35.185561 -97.398361
  • Price College Digital LibraryBorrow it
    Adams Hall 102 307 West Brooks St., Norman, OK, 73019, US
    35.210371 -97.448244
  • Western History CollectionsBorrow it
    Monnet Hall 630 Parrington Oval, Rm. 300, Norman, OK, 73019, US
    35.209584 -97.445414
Processing Feedback ...