Global Analysis of Dynamical Systems: Festschrift dedicated to Floris Takens for his 60th birthday
Purchasing Options
Summary
Contributed by close colleagues, friends, and former students of Floris Takens, Global Analysis of Dynamical Systems is a liber amicorum dedicated to Takens for his 60th birthday. The first chapter is a reproduction of Takens's 1974 paper "Forced oscillators and bifurcations" that was previously available only as a preprint of the University of Utrecht. Among other important results, it contains the unfolding of what is now known as the Bogdanov-Takens bifurcation. The remaining chapters cover topics as diverse as bifurcation theory, Hamiltonian mechanics, homoclinic bifurcations, routes to chaos, ergodic theory, renormalization theory, and time series analysis. In its entirety, the book bears witness to the influence of Takens on the modern theory of dynamical systems and its applications. This book is a must-read for anyone interested in this active and exciting field.
Table of Contents
Preface. 1 Forced oscillations and bifurcations Floris Takens. 2 Historical behaviour in smooth dynamical systems David Ruelle. References. 3 Implicit formalism for affine-like maps and parabolic composition Jacob Palis and Jean-Christophe Yoccoz. On Floris as a friend. 3-1 On homoclinic bifurcations. 3-2 Implicit formalism for affine-like maps. 3-3 Parabolic composition. References. 4 Strong resonances and Takens's Utrecht preprint Bernd Krauskopf. 4-1 Setting and notation. 4-2 Zq-equivariant normal forms. 4-3 Weak resonance. 4-4 Strong resonances. 4-5 Strong resonance for q = 4. 4-6 From the normal form to the full dynamics. References. 5 Semi-local analysis of the k : 1 and k : 2 resonances in quasi-periodically forced systems Florian Wagener. 5-1 Preliminaries. 5-2 Normal form analysis. 5-3 Semi-local bifurcation analysis of the k: 1 resonance. 5-4 Semi-local bifurcation analysis of the k: 2 resonance. 5-5 Conclusions.vi . Acknowledgements. References. 6 Generic unfolding of the nilpotent saddle of codimension four Freddy Dumortier, Peter Fiddelaers and Chengzhi Li. 7 Exponential confinement of chaos in the bifurcation sets of real analytic difeomorphisms. 8 Takens-Bogdanov bifurcations without parameters and oscillatory shock profiles. 9 Global birfurcations of periodic orbits in the forced Van der Pol equation. 10 An unfolding theory approach to bursting in fast-slow systems. 11 The intermittency route to chaotic dynamics. 12 Homoclinic points in complex dynamical systems. Excitation of elliptic normal modes of invariant tori in volume perserving flows. 14 On the global dynamics of Kirchhoff's equations: rigid body models for underwater vehicles. 15 Global dynamics and fast indicators. 16 A general nonparametric bootstrap test for Granger causality. 17 Birkhoff averages and bifurcations. 18 The multifractal analysis of Birkhoff averages and large deviations. 19 Existence of absolutely continuous invariant probability measures for multimodal maps. 20 On the dynamics of the renormalization operator. Index
Editorial Reviews
"This book covers a great variety of topics in dynamical systems reflecting the wide interest and many scientific contacts of Floris Takens. He wrote seminal papers on singularities of vector fields, bifurcation theory, reconstruction in time-series analysis, and many other subjects. It was a good idea to start with the reprint of an early and influential publication by Takens: Forced Oscillations and Bifurcations. In 20 papers the text ranges from the pure mathematical side of dynamical systems to applications, including a note by Ruelle, a paper by long-term collaborators Palis and Yoccoz, and interesting accounts of work by former students and friends. There are many more interesting papers in this Festschrift. It is not only a nice tribute to Floris Takens but at the same time a valuable and stimulating addition to the dynamical systems literature."
-Dynamical Systems Magazine
