LEADER 01018nam2-2200361---450- 001 990001451560203316 005 20050308140607.0 035 $a000145156 035 $aUSA01000145156 035 $a(ALEPH)000145156USA01 035 $a000145156 100 $a20040225d1978----km-y0itay0103----ba 101 0 $aita 102 $aIT 105 $aa|||||||001yy 200 1 $a<<2.17>> : Basilicata 210 $aSan Lorenzo in Campo$cGeotecneco (Gruppo Eni)$d1978 215 $a269 p.$cill., 1 c. geogr.$d27 cm 410 0$12001 454 1$12001 461 1$1001000145120$12001$aMonografie regionali 607 $aBasilicata$xZone montane 676 $a914.5 801 0$aIT$bsalbc$gISBD 912 $a990001451560203316 951 $aIII.1. 1916/2.17 (I L 160/17)$b7302 L.M.$cI L 959 $aBK 969 $aUMA 979 $aSIAV4$b10$c20040225$lUSA01$h0955 979 $aPATRY$b90$c20040406$lUSA01$h1742 979 $aCOPAT4$b90$c20050308$lUSA01$h1406 996 $aBasilicata$955646 997 $aUNISA LEADER 05706nam 2200757Ia 450 001 9910458099103321 005 20200520144314.0 010 $a1-281-86756-X 010 $a9786611867560 010 $a1-86094-854-5 035 $a(CKB)1000000000399735 035 $a(EBL)1679366 035 $a(OCoLC)748530877 035 $a(SSID)ssj0000142031 035 $a(PQKBManifestationID)11148714 035 $a(PQKBTitleCode)TC0000142031 035 $a(PQKBWorkID)10090561 035 $a(PQKB)11059851 035 $a(MiAaPQ)EBC1679366 035 $a(WSP)0000P515 035 $a(PPN)168273195 035 $a(Au-PeEL)EBL1679366 035 $a(CaPaEBR)ebr10255948 035 $a(CaONFJC)MIL186756 035 $a(EXLCZ)991000000000399735 100 $a20070728d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDynamics and symmetry$b[electronic resource] /$fMichael J. Field 210 $aLondon $cImperial College Press ;$aSingapore ;$aHackensack, NJ $cDistributed by World Scientific$dc2007 215 $a1 online resource (492 p.) 225 1 $aICP advanced texts in mathematics,$x1753-657X ;$vv. 3 300 $aDescription based upon print version of record. 311 $a1-86094-828-6 320 $aIncludes bibliographical references (p. 457-466) and indexes. 327 $aContents; Preface; 1. Groups; 1.1 Definition of a group and examples; 1.2 Homomorphisms, subgroups and quotient groups; 1.2.1 Generators and relations for .nite groups; 1.3 Constructions; 1.4 Topological groups; 1.5 Lie groups; 1.5.1 The Lie bracket of vector fields; 1.5.2 The Lie algebra of G; 1.5.3 The exponential map of g; 1.5.4 Additional properties of brackets and exp; 1.5.5 Closed subgroups of a Lie group; 1.6 Haarmeasure; 2. Group Actions and Representations; 2.1 Introduction; 2.2 Groups and G-spaces; 2.2.1 Continuous actions and G-spaces; 2.3 Orbit spaces and actions 327 $a2.4 Twisted products2.4.1 Induced G-spaces; 2.5 Isotropy type and stratification by isotropy type; 2.6 Representations; 2.6.1 Averaging over G; 2.7 Irreducible representations and the isotypic decomposition; 2.7.1 C-representations; 2.7.2 Absolutely irreducible representations; 2.8 Orbit structure for representations; 2.9 Slices; 2.9.1 Slices for linear finite group actions; 2.10 Invariant and equivariant maps; 2.10.1 Smooth invariant and equivariant maps on representations; 2.10.2 Equivariant vector fields and flows; 3. Smooth G-manifolds; 3.1 Proper G-manifolds; 3.1.1 Proper free actions 327 $a3.2 G-vector bundles3.3 Infinitesimal theory; 3.4 Riemannianmanifolds; 3.4.1 Exponential map of a complete Riemannian manifold; 3.4.2 The tubular neighbourhood theorem; 3.4.3 Riemannian G-manifolds; 3.5 The differentiable slice theorem; 3.6 Equivariant isotopy extension theorem; 3.7 Orbit structure for G-manifolds; 3.7.1 Closed filtration of M by isotropy type; 3.8 The stratification of M by normal isotropy type; 3.9 Stratified sets; 3.9.1 Transversality to a Whitney stratification; 3.9.2 Regularity of stratification by normal isotropy type 327 $a3.10 Invariant Riemannian metrics on a compact Lie group3.10.1 The adjoint representations; 3.10.2 The exponential map; 3.10.3 Closed subgroups of a Lie group; 4. Equivariant Bifurcation Theory: Steady State Bifurcation; 4.1 Introduction and preliminaries; 4.1.1 Normalized families; 4.2 Solution branches and the branching pattern; 4.2.1 Stability of branching patterns; 4.3 Symmetry breaking-theMISC; 4.3.1 Symmetry breaking isotropy types; 4.3.2 Maximal isotropy subgroup conjecture; 4.4 Determinacy; 4.4.1 Polynomial maps; 4.4.2 Finite determinacy; 4.5 The hyperoctahedral family 327 $a4.5.1 The representations (Rk,Hk)4.5.2 Invariants and equivariants for Hk; 4.5.3 Cubic equivariants for Hk; 4.5.4 Bifurcation for cubic families; 4.5.5 Subgroups of Hk; 4.5.6 Some subgroups of the symmetric group; 4.5.7 A big family of counterexamples to the MISC; 4.5.8 Examples where P3G (Rk, Rk) = P3H k (Rk, Rk); 4.5.9 Stable solution branches of maximal index and trivial isotropy; 4.5.10 An example with applications to phase transitions; 4.6 Phase vector field and maps of hyperbolic type; 4.6.1 Cubic polynomial maps; 4.6.2 Phase vector field; 4.6.3 Normalized families 327 $a4.6.4 Maps of hyperbolic type 330 $a This book contains the first systematic exposition of the global and local theory of dynamics equivariant with respect to a (compact) Lie group. Aside from general genericity and normal form theorems on equivariant bifurcation, it describes many general families of examples of equivariant bifurcation and includes a number of novel geometric techniques, in particular, equivariant transversality. This important book forms a theoretical basis of future work on equivariant reversible and Hamiltonian systems. This book also provides a general and comprehensive introduction to codimension one equi 410 0$aImperial College Press advanced texts in mathematics ;$vv. 3. 606 $aTopological dynamics 606 $aLie groups 606 $aHamiltonian systems 606 $aBifurcation theory 606 $aSymmetry (Mathematics) 608 $aElectronic books. 615 0$aTopological dynamics. 615 0$aLie groups. 615 0$aHamiltonian systems. 615 0$aBifurcation theory. 615 0$aSymmetry (Mathematics) 676 $a515.35 700 $aField$b Mike$056769 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910458099103321 996 $aDynamics and symmetry$92242656 997 $aUNINA