On the topology of nearly-integrable Hamiltonians at simple resonances

  title={On the topology of nearly-integrable Hamiltonians at simple resonances},
  author={Luca Biasco and Luigi Chierchia},
We show that, in general, averaging at simple resonances a real--analytic, nearly--integrable Hamiltonian, one obtains a one--dimensional system with a cosine--like potential; ``in general'' means for a generic class of holomorphic perturbations and apart from a finite number of simple resonances with small Fourier modes; ``cosine--like'' means that the potential depends only on the resonant angle, with respect to which it is a Morse function with one maximum and one minimum. \\ Furthermore… 
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Action-angle Variables for Generic 1D Mechanical Systems.
We consider a 1D mechanical system $$\bar {\mathtt H}(\mathtt P,\mathtt Q)=\mathtt P^2+\bar {\mathtt G}(\mathtt Q)$$ in action-angle variable $(\mathtt P,\mathtt Q)$ where $\bar {\mathtt G}$ is a
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Prevalence of exponential stability among nearly integrable Hamiltonian systems
  • L. Niederman
  • Mathematics
    Ergodic Theory and Dynamical Systems
  • 2007
In the 1970s, Nekhorochev proved that, for an analytic nearly integrable Hamiltonian system, the action variables of the unperturbed Hamiltonian remain nearly constant over an exponentially long time
Rigorous estimates for the series expansions of Hamiltonian perturbation theory
In the present paper we prove a theorem giving rigorous estimates in the problem of bringing to normal form a nearly integrable Hamiltonian system, using methods of classical perturbation theory,
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We prove the existence of Arnold diffusion in a typical a priori unstable Hamiltonian system outside a small neighbourhood of strong resonances. More precisely, we consider a near-integrable
Drift and diffusion in phase space
The problem of stability of action variables (i.e. of the adiabatic invariants) in perturbations of completely integrable (real analytic) hamiltonian systems with more than two degrees of freedom is
Diffusion and stability in perturbed non-convex integrable systems
The Nekhoroshev theorem has become an important tool for explaining the long-term stability of many quasi-integrable systems of interest in physics. The action variables of systems that satisfy the
Estimates in the kolmogorov theorem on conservation of conditionally periodic motions
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Existence of Diffusion Orbits in a priori Unstable Hamiltonian Systems
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Effective Stability and KAM Theory
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In the present paper we give a proof of Nekhoroshev's theorem, which is concerned with an exponential estimate for the stability times in nearly integrable Hamiltonian systems. At variance with the