- Acta Math.
- Volume 217, Number 1 (2016), 1-79.
Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders
We prove a form of Arnold diffusion in the a-priori stable case. Let be a nearly integrable system of arbitrary degrees of freedom with a strictly convex H0. We show that for a “generic” , there exists an orbit satisfying where is independent of . The diffusion orbit travels along a codimension-1 resonance, and the only obstruction to our construction is a finite set of additional resonances.
For the proof we use a combination of geometric and variational methods, and manage to adapt tools which have recently been developed in the a-priori unstable case.
Acta Math., Volume 217, Number 1 (2016), 1-79.
Received: 4 April 2013
Revised: 28 September 2016
First available in Project Euclid: 22 February 2017
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Bernard, Patrick; Kaloshin, Vadim; Zhang, Ke. Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders. Acta Math. 217 (2016), no. 1, 1--79. doi:10.1007/s11511-016-0141-5. https://projecteuclid.org/euclid.acta/1487789798