Handbook of Dynamical Systems

Presents a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics

H. Broer (Edited by), F. Takens (Edited by), B. Hasselblatt (Edited by)

9780444638212, Elsevier Science

Paperback / softback, published 19 August 2016

560 pages
22.9 x 15.1 x 3.5 cm, 0.67 kg

In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli.

1. Introduction, 2. Complex linearization, 3. KAM Theory for circle and annulus maps, 4. KAM Theory for flows, 5. Further developments in KAM Theory, 6. Quasi-periodic bifurcations: dissipative setting, 7. Quasi-periodic bifurcation theory in other settings, 8. Further Hamiltonian KAM Theory, 9. Whitney smooth bundles of KAM tori, 10. Conclusion

Subject Areas: Geometry [PBM]