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**Elements of applied bifurcation theory.
2nd updated ed.**
*(English)*
Zbl 0914.58025

Applied Mathematical Sciences. 112. New York, NY: Springer. xix, 591 p. (1998).

This is the second edition of a textbook the contents of which are described in the review of the first edition (Zbl 0829.58029), or more exhaustively in the preface of the book itself. After two chapters on fundamental notions, seven chapters deal with bifurcations in increasingly more complicated situations: One- and two-parameter bifurcations of stationary points in finite-dimensional continuous and discrete dynamical systems as well as bifurcations of homoclinic and heteroclinic orbits. The latter material has been rewritten for this edition. A final chapter on numerical analysis also has been changed to include more refined methods as well as an updated software review. Other changes aim at making the work more comprehensive and complete. Every chapter is followed by exercises and bibliographical notes. The combination of theoretical results and applications to concrete examples makes this book a most expansive introduction to the subject.

Reviewer: D.Erle (Dortmund)

### MSC:

37G99 | Local and nonlocal bifurcation theory for dynamical systems |

37-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory |

37G05 | Normal forms for dynamical systems |

34C23 | Bifurcation theory for ordinary differential equations |