Global Analysis of Dynamical Systems

Abstract

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