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Home > Mathematics and Science Textbooks > Physics > Global Analysis of Dynamical Systems: Festschrift dedicated to Floris Takens for his 60th birthday(English)
Global Analysis of Dynamical Systems: Festschrift dedicated to Floris Takens for his 60th birthday(English)

Global Analysis of Dynamical Systems: Festschrift dedicated to Floris Takens for his 60th birthday(English)

          
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About the Book

This volume is a "liber amicorum", offered to Floris Takens on the occasion of his 60th birthday. The contributions are written by close colleagues, friends and former students of Floris Takens. Chapter One of the book is a reproduction of Taken's 1974 paper, "Forced Oscillators and Bifurcations", that was previously available only as a preprint of the University of Utrecht. It included the unfolding of what is now known as the Bogdanov-Takens bifurcation. The other chapters are contributions by experts covering 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 Floris Takens on the modern theory of Dynamical Systems and its applications. At the same time, it contains many research papers, all connected to certain aspects of Taken's work.

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


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Product Details
  • ISBN-13: 9780750308038
  • Publisher: Taylor & Francis Ltd
  • Publisher Imprint: Institute of Physics Publishing
  • Edition: 1st
  • Language: English
  • Returnable: N
  • Spine Width: 29 mm
  • Weight: 953 gr
  • ISBN-10: 0750308036
  • Publisher Date: 18 Jun 2001
  • Binding: Hardback
  • Height: 229 mm
  • No of Pages: 464
  • Series Title: English
  • Sub Title: Festschrift dedicated to Floris Takens for his 60th birthday
  • Width: 152 mm


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