The existence of invariant tori of reversible systems with Liouvillean frequency and its applications

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Cites Work

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Construction of response solutions for two classes of quasi-periodically forced four-dimensional nonlinear systems with degenerate equilibrium point under small perturbations
A KAM scheme for SL(2, \(\mathbb R\)) cocycles with Liouvillean frequencies
Invariant m-dimensional tori of reversible systems with phase space of dimension greater than 2m
Elliptic-type degenerate invariant tori for quasi-periodically forced four-dimensional non-conservative systems
Almost reducibility and non-perturbative reducibility of quasi-periodic linear systems
On a quasi-periodic Hopf bifurcation
Quasi-periodic response solutions in forced reversible systems with Liouvillean frequencies
Persistence of hyperbolic-type degenerate lower-dimensional invariant tori with prescribed frequencies in Hamiltonian systems
Response solutions for quasi-periodically forced harmonic oscillators
The iteration-approximation decoupling in the reversible KAM theory
Response solutions and quasi-periodic degenerate bifurcations for quasi-periodically forced systems
Stoker's Problem for Quasi-periodically Forced Reversible Systems with Multidimensional Liouvillean Frequency
Reducibility of a class of nonlinear quasi-periodic systems with Liouvillean basic frequencies
Partial preservation of frequencies in KAM theory
Combination tones for Duffing's equation
Quasi-periodic solutions of nonlinear ordinary differential equations with small damping
Persistence of lower dimensional degenerate invariant tori with prescribed frequencies in Hamiltonian systems with small parameter
On lower dimensional invariant tori in reversible systems
Persistence of multiscale degenerate invariant tori for reversible systems with multiscale degenerate equilibrium points
The persistence of degenerate lower-dimensional tori in reversible systems with a degenerate normal equilibrium point
Response solutions for finite smooth harmonic oscillators with quasi-periodic forcing

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