Destruction of invariant circles for Gevrey area-preserving twist maps

Abstract

In this paper, we show that for exact area-preserving twist maps on annulus, the invariant circles with a given rotation number can be destroyed by arbitrarily small Gevrey-$\alpha$ perturbations of the integrable generating function in the $C^r$ topology with $r<4-\frac{2}{\alpha }$, where $\alpha >1$.

to appear in Journal of Dynamics and Differential Equations (JDDE). arXiv admin note: text overlap with arXiv:1208.2840, arXiv:1106.6137

Cited by in corpus (2)

• Gevrey genericity of Arnold diffusion in a priori unstable Hamiltonian systems
• Quantitative destruction of invariant circles