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Quasi-Periodic Motions in Families of Dynamical Systems: Order amidst Chaos
and examples.- The conjugacy theory.- The continuation theory.- Complicated Whitney-smooth families.- Conclusions.- Appendices.
Quasi-periodic motions in families of dynamical systems
Unfoldings and Bifurcations of Quasi-Periodic Tori
Quasi-periodic bifurcations of invariant circles in low-dimensional dissipative dynamical systems
This paper first summarizes the theory of quasi-periodic bifurcations for dissipative dynamical systems. Then it presents algorithms for the computation and continuation of invariant circles and of… Expand
Subordinate Sil'nikov bifurcations near some singularities of vector fields having low codimension
A specific singularity of a vector field on R 3 is considered, of codimension 2 in the dissipative case and of codimension 1 in the conservative case. In both contexts in generic unfoldings the… Expand
Families of quasi-periodic motions in dynamical systems depending on parameters
One of the central topics in the qualitative theory of differential equations is the study of invariant submanifolds. A number of general theorems establishing the existence and/or persistence and… Expand
Handbook of Dynamical Systems
Volume 1A. Principal structures (B. Hasselblatt, A. Katok). Entropy, Isomorphism and Equivalence (J.-P. Thouvenot). Hyperbolic dynamics (B. Hasselblatt). Invariant measures for hyperbolic dynamical… Expand
Invariant circles in the Bogdanov-Takens bifurcation for diffeomorphisms
We study a generic, real analytic unfolding of a planar diffeomorphism having a fixed point with unipotent linear part. In the analogue for vector fields an open parameter-domain is known to exist,… Expand