Invariant curves of quasi-periodic reversible mappings and its application
Copyright policy )Invariant curves of quasi-periodic reversible mappings and its application
We consider the existence of invariant curves of real analytic reversible mappings which are quasi-periodic in the angle variables. By the normal form theorem, we prove that under some assumptions, the original mapping is changed into its linear part via an analytic convergent transformation, so that invariants curves are obtained. In the iterative process, by solving the modified homological equations, we ensure that the transformed mapping is still reversible. As an application, we investigate the invariant curves of a class of nonlinear resonant oscillators, with the Birkhoff constants of the corresponding Poincar$\acute{e}$ mapping all zeros or not.
- Ocean University of China China (People's Republic of)
Dynamical aspects of twist maps, invariant curves, reversible mappings, normal forms, FOS: Mathematics, Periodic orbits of vector fields and flows, Nonlinear oscillations and coupled oscillators for ordinary differential equations, quasi-periodic solutions, Periodic and quasi-periodic flows and diffeomorphisms, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces, Birkhoff constants
Dynamical aspects of twist maps, invariant curves, reversible mappings, normal forms, FOS: Mathematics, Periodic orbits of vector fields and flows, Nonlinear oscillations and coupled oscillators for ordinary differential equations, quasi-periodic solutions, Periodic and quasi-periodic flows and diffeomorphisms, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces, Birkhoff constants
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