On asymptotically periodic-like motions in flows

On bifurcations into nonresonant quasi-periodic motions

The stability, instability, and bifurcation behaviour of a nonlinear autonomous system in the vicinity of a compound critical point is studied in detail. The critical point is characterized by two distinct pairs of pure imaginary eigenvalues of the Jacobian, and the system is described by two independent parameters. The analysis is based on a generalized perturbation procedure which employs mul...

Expansions Forquasi Periodic Motions

Asymptotically Conformal Fixed Points and Holomorphic Motions

The term integrable asymptotically conformal at a point for a quasiconformal map defined on a domain is defined. Furthermore, we prove that there is a normal form for this kind attracting or repelling or superattracting fixed point with the control condition under a quasiconformal change of coordinate which is also asymptotically conformal at this fixed point. The change of coordinate is essent...

Piecewise Contractions Are Asymptotically Periodic

We show that, given a finite partition of the plane C such that the map G acts as a linear contraction on each part, for almost every choice of parameters every orbit of G is (asymptotically) periodic.

Asymptotic Behavior for Asymptotically Periodic

The properties of ω-limit set and global asymptotic behavior are first obtained for asymptotically autonomous discrete dynamical processes on metric spaces.Then certain equivalence of the asymptotic behavior between an asymptotically periodic semiflows and its associated asymptotically autonomous discrete dynamical process is proved. As some applications, the global behavior of asymptotically p...