Equivariant Degree Theory / / Jorge Ize, Alfonso Vignoli.
This book presents a new degree theory for maps which commute with a group of symmetries. This degree is no longer a single integer but an element of the group of equivariant homotopy classes of maps between two spheres and depends on the orbit types of the spaces. The authors develop completely the...
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| Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2008] ©2003 |
| Year of Publication: | 2008 |
| Edition: | Reprint 2012 |
| Language: | English |
| Series: | De Gruyter Series in Nonlinear Analysis and Applications ,
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| Physical Description: | 1 online resource (361 p.) |
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Ize, Jorge, author. aut http://id.loc.gov/vocabulary/relators/aut Equivariant Degree Theory / Jorge Ize, Alfonso Vignoli. Reprint 2012 Berlin ; Boston : De Gruyter, [2008] ©2003 1 online resource (361 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Series in Nonlinear Analysis and Applications , 0941-813X ; 8 Frontmatter -- Contents -- Chapter 1. Preliminaries -- Chapter 2. Equivariant Degree -- Chapter 3. Equivariant Homotopy Groups of -- Spheres -- Chapter 4. Equivariant Degree and -- Applications -- Backmatter restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star This book presents a new degree theory for maps which commute with a group of symmetries. This degree is no longer a single integer but an element of the group of equivariant homotopy classes of maps between two spheres and depends on the orbit types of the spaces. The authors develop completely the theory and applications of this degree in a self-contained presentation starting with only elementary facts. The first chapter explains the basic tools of representation theory, homotopy theory and differential equations needed in the text. Then the degree is defined and its main abstract properties are derived. The next part is devoted to the study of equivariant homotopy groups of spheres and to the classification of equivariant maps in the case of abelian actions. These groups are explicitely computed and the effects of symmetry breaking, products and composition are thorougly studied. The last part deals with computations of the equivariant index of an isolated orbit and of an isolated loop of stationary points. Here differential equations in a variety of situations are considered: symmetry breaking, forcing, period doubling, twisted orbits, first integrals, gradients etc. Periodic solutions of Hamiltonian systems, in particular spring-pendulum systems, are studied as well as Hopf bifurcation for all these situations. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) Homotopy groups. Topological degree. Gewöhnliche Differentialgleichung. Globale Analysis. MATHEMATICS / General. bisacsh Vignoli, Alfonso, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter DG Studies in Nonlinear Analysis and Applications 9783110647099 Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 9783110238570 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) 9783110238471 Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 9783110637205 ZDB-23-GMA Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2008 9783110212129 ZDB-23-DGG Title is part of eBook package: De Gruyter E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2008 9783110212136 Title is part of eBook package: De Gruyter E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2008 9783110209082 ZDB-23-DMN Title is part of eBook package: De Gruyter E-DITION 2: BEST OF MATHEMATICS, PHYSICS 9783110306569 ZDB-23-DBI print 9783110175509 https://doi.org/10.1515/9783110200027 https://www.degruyter.com/isbn/9783110200027 Cover https://www.degruyter.com/document/cover/isbn/9783110200027/original |
| language |
English |
| format |
eBook |
| author |
Ize, Jorge, Ize, Jorge, Vignoli, Alfonso, |
| spellingShingle |
Ize, Jorge, Ize, Jorge, Vignoli, Alfonso, Equivariant Degree Theory / De Gruyter Series in Nonlinear Analysis and Applications , Frontmatter -- Contents -- Chapter 1. Preliminaries -- Chapter 2. Equivariant Degree -- Chapter 3. Equivariant Homotopy Groups of -- Spheres -- Chapter 4. Equivariant Degree and -- Applications -- Backmatter |
| author_facet |
Ize, Jorge, Ize, Jorge, Vignoli, Alfonso, Vignoli, Alfonso, Vignoli, Alfonso, |
| author_variant |
j i ji j i ji a v av |
| author_role |
VerfasserIn VerfasserIn VerfasserIn |
| author2 |
Vignoli, Alfonso, Vignoli, Alfonso, |
| author2_variant |
a v av |
| author2_role |
VerfasserIn VerfasserIn |
| author_sort |
Ize, Jorge, |
| title |
Equivariant Degree Theory / |
| title_full |
Equivariant Degree Theory / Jorge Ize, Alfonso Vignoli. |
| title_fullStr |
Equivariant Degree Theory / Jorge Ize, Alfonso Vignoli. |
| title_full_unstemmed |
Equivariant Degree Theory / Jorge Ize, Alfonso Vignoli. |
| title_auth |
Equivariant Degree Theory / |
| title_alt |
Frontmatter -- Contents -- Chapter 1. Preliminaries -- Chapter 2. Equivariant Degree -- Chapter 3. Equivariant Homotopy Groups of -- Spheres -- Chapter 4. Equivariant Degree and -- Applications -- Backmatter |
| title_new |
Equivariant Degree Theory / |
| title_sort |
equivariant degree theory / |
| series |
De Gruyter Series in Nonlinear Analysis and Applications , |
| series2 |
De Gruyter Series in Nonlinear Analysis and Applications , |
| publisher |
De Gruyter, |
| publishDate |
2008 |
| physical |
1 online resource (361 p.) Issued also in print. |
| edition |
Reprint 2012 |
| contents |
Frontmatter -- Contents -- Chapter 1. Preliminaries -- Chapter 2. Equivariant Degree -- Chapter 3. Equivariant Homotopy Groups of -- Spheres -- Chapter 4. Equivariant Degree and -- Applications -- Backmatter |
| isbn |
9783110200027 9783110647099 9783110238570 9783110238471 9783110637205 9783110212129 9783110212136 9783110209082 9783110306569 9783110175509 |
| issn |
0941-813X ; |
| callnumber-first |
Q - Science |
| callnumber-subject |
QA - Mathematics |
| callnumber-label |
QA612 |
| callnumber-sort |
QA 3612 I94 42003EB |
| url |
https://doi.org/10.1515/9783110200027 https://www.degruyter.com/isbn/9783110200027 https://www.degruyter.com/document/cover/isbn/9783110200027/original |
| illustrated |
Not Illustrated |
| dewey-hundreds |
500 - Science |
| dewey-tens |
510 - Mathematics |
| dewey-ones |
514 - Topology |
| dewey-full |
514/.2 |
| dewey-sort |
3514 12 |
| dewey-raw |
514/.2 |
| dewey-search |
514/.2 |
| doi_str_mv |
10.1515/9783110200027 |
| oclc_num |
979752994 |
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AT izejorge equivariantdegreetheory AT vignolialfonso equivariantdegreetheory |
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(DE-B1597)32453 (OCoLC)979752994 |
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Equivariant Degree Theory / |
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