## Journal of Differential Geometry

### Uniform hyperbolicity of invariant cylinder

Chong-Qing Cheng

#### Abstract

For a positive definite Hamiltonian system $H = h(p) + \epsilon P (p, q)$ with $(p, q) \in \mathbb{R}^3 \times \mathbb{T}^3$, large normally hyperbolic invariant cylinders exist along the whole resonant path, except for the $\epsilon^{\frac{1}{2}+d}$ neighborhood of finitely many double resonant points. It allows one to construct diffusion orbits to cross double resonance.

#### Article information

Source
J. Differential Geom., Volume 106, Number 1 (2017), 1-43.

Dates
First available in Project Euclid: 26 April 2017

https://projecteuclid.org/euclid.jdg/1493172093

Digital Object Identifier
doi:10.4310/jdg/1493172093

Mathematical Reviews number (MathSciNet)
MR3640006

Zentralblatt MATH identifier
06731735

#### Citation

Cheng, Chong-Qing. Uniform hyperbolicity of invariant cylinder. J. Differential Geom. 106 (2017), no. 1, 1--43. doi:10.4310/jdg/1493172093. https://projecteuclid.org/euclid.jdg/1493172093