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Full Product Details

Author:   H.W Broer ,  B Krauskopf (Bristol University, UK) ,  Gert Vegter (University of Groningen, The Netherlands)
Publisher:   Taylor & Francis Ltd
Imprint:   Institute of Physics Publishing
Dimensions:   Width: 15.20cm , Height: 3.00cm , Length: 22.90cm
Weight:   0.953kg
ISBN:  

9780750308038

ISBN 10:   0750308036
Pages:   464
Publication Date:   18 June 2001
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Out of Print
Availability:   Out of stock  

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

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, 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 ok 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, 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 thedynamical systems literature. Dynamical Systems Magazine

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