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- W1511274701 abstract "We present Kolmogorov–Arnold–Moser (or KAM) Theory regarding typicality of quasi-periodic invariant tori, partly from a historical and partly from a pedagogical point of view. At the same time we aim at a unified approach of the theory in various dynamical settings: the ‘classical’ Hamiltonian setting of Lagrangean tori, the Hamiltonian lower dimensional isotropic tori, the dissipative case of quasi-periodic attractors, etc. Also we sketch the theory of quasi-periodic bifurcations, where resonances cause Cantorization and fraying of the bifurcation sets known from the cases of equilibrium points and periodic orbits. Here the concept of Whitney differentiability plays a central role, which locally organizes the nowhere dense union of persistent quasi-periodic invariant tori, of positive measure. At the level of torus bundles this Cantorization is observed as well, where the geometry of the torus bundles turns out to be persistent. In the meantime we briefly deal with the natural affine structure of quasi-periodic tori, with uniqueness of most of the KAM tori, and with the mechanisms of the destruction of resonant unperturbed tori. Other parts of the theory, such as the Hamiltonian higher" @default.
- W1511274701 created "2016-06-24" @default.
- W1511274701 creator A5041196265 @default.
- W1511274701 creator A5069925617 @default.
- W1511274701 date "2010-01-01" @default.
- W1511274701 modified "2023-10-14" @default.
- W1511274701 title "KAM Theory: Quasi-periodicity in Dynamical Systems" @default.
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