Handbook of Dynamical Systems

In this volume, the authors of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they can be active in the coming years. The surveys are intended to educate the reader on the subject of transience and generic properties of the so-called Kupka-Smale theorem, the Closing Lemma and the generic local bifurcations of functions (so-called catastrophe theory ) and generic local bifurcations in 1-parameter families of dynamical systems.

• Covers recent literature on the topic of differentiable dynamical systems


• Highlights developments that are the foundation for future research in this field


• Provides in the form of differentiable dynamical systems

1. Introduction, 2. Complex linearization, 3. KAM Theory for circle and annulus maps, 4. KAM Theory for flows, 5. Further development 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