Singularities, Bifurcations and CatastrophesCambridge University Press, 24 de juny 2021 Suitable for advanced undergraduates, postgraduates and researchers, this self-contained textbook provides an introduction to the mathematics lying at the foundations of bifurcation theory. The theory is built up gradually, beginning with the well-developed approach to singularity theory through right-equivalence. The text proceeds with contact equivalence of map-germs and finally presents the path formulation of bifurcation theory. This formulation, developed partly by the author, is more general and more flexible than the original one dating from the 1980s. A series of appendices discuss standard background material, such as calculus of several variables, existence and uniqueness theorems for ODEs, and some basic material on rings and modules. Based on the author's own teaching experience, the book contains numerous examples and illustrations. The wealth of end-of-chapter problems develop and reinforce understanding of the key ideas and techniques: solutions to a selection are provided. |
Continguts
| 1 | |
Part I Catastrophe theory | 17 |
Part II Singularity theory | 123 |
Part III Bifurcation theory | 217 |
Part IV Appendices | 313 |
| 417 | |
| 425 | |
Altres edicions - Mostra-ho tot
Frases i termes més freqüents
algebraic applications argument assume basis bifurcation problem bifurcation theory called catastrophe Chapter classification cobasis codimension component condition consider constant contact equivalence contains coordinates core corresponding critical point curve cusp defined definition degenerate denote derivatives described determined diagram diffeomorphism differential dimension discriminant discussed elements equal equation equivalence example 𝑓 fact Figure finite finite codimension finite determinacy follows function given gives ideal important invertible lemma linear lines map germ matrix means module neighbourhood nondegenerate Note origin parameter particular path plane polynomial proof Proposition prove rank relation representative respect result ring satisfying Show similar simple singularity smooth smooth function smooth map solutions submanifold submersion subset Suppose surface tangent space theorem theory values variables variety vector fields versal unfolding write zero